Content-Type: multipart/mixed; boundary="-------------9903190313174" This is a multi-part message in MIME format. ---------------9903190313174 Content-Type: text/plain; name="99-82.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="99-82.keywords" group integrals, coupling coefficients, 6j-symbols ---------------9903190313174 Content-Type: application/postscript; name="6j_symbol.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="6j_symbol.ps" %!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: 6j_symbol.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSCommandLine: dvips 6j_symbol %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 1999.03.19:1107 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 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Fq(\()p Fp(`)1362 4484 y Fn(1)1402 4469 y Fp(;)17 b(`)1487 4484 y Fn(2)1526 4469 y Fp(;)g(`)1611 4484 y Fn(3)1650 4469 y Fu(j)p Fp(`)1719 4484 y Fn(4)1758 4469 y Fp(;)g(`)1843 4484 y Fn(5)1882 4469 y Fp(;)g(`)1967 4484 y Fn(6)2006 4469 y Fq(\).)0 4752 y Fv(2.)50 b(Explicit)34 b(in)m(tegration)i(of)h(\(1\))0 4984 y Fq(In)32 b(this)f(section)g(w)m(e)i(will)c(mak)m(e)i(extensiv)m (e)j(use)e(of)f(our)g(previous)h(results)g([1].)43 b(In)32 b(the)f(follo)m(wing)e(if)0 5116 y(w)m(e)k(refer)f(to)f(equations)h(of) f(ref)h([1])g(w)m(e)g(will)e(add)h(the)h(subscript)h(1)e(to)h(the)g (equation)f(n)m(um)m(b)s(er.)44 b(F)-8 b(or)0 5249 y(example,)41 b(\(18\))592 5213 y Fn(1)670 5249 y Fq(refers)g(to)e(eq)i(\(18\))e(of)g ([1])g(whic)m(h)h(sho)m(ws)i(that)d(the)h(zonal)f(spherical)g (functions)0 5382 y(can)e(b)s(e)g(expressed)j(in)c(terms)h(of)f(Gegen)m (bauer)i(p)s(olynomials.)53 b(In)38 b(fact,)g(using)e(this)h(relation)e (the)p eop %%Page: 3 3 3 2 bop 0 17 a Fh(Coupling)34 b(c)-5 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Fi(x)46 b Ft(A)24 b Fd(Mathematic)l(a)h Ft(pac)n(k)-5 b(age)22 b(whic)n(h)h(implemen)n(ts)h(the)g(results)f(of)g(this)h(pap)r (er)f(can)g(b)r(e)h(obtained)f(from)g(the)h(authors)0 5712 y(up)r(on)k(request.)p eop %%Page: 6 6 6 5 bop 0 17 a Fh(Coupling)34 b(c)-5 b(o)g(e\016cients)34 b(of)g(SO\(n\))2370 b Fq(6)42 232 y Ft([3])41 b(Jo)n(yce)26 b(G)i(S)f(1967)f Fd(Phys.)31 b(R)l(ev.)d Fs(155)f Ft(478-491)42 340 y([4])41 b(Dom)n(b)27 b(C)h(1972)e Fd(J.)j(Phys.)j(A:)d(Math.)i (Gen.)e Fs(5)e Ft(1417-1428)42 448 y([5])41 b(Cucc)n(hieri)27 b(A,)h(Mendes)f(T,)h(P)n(elissetto)e(A)i(and)g(Sok)-5 b(al)27 b(A)h(D)g(1997)d Fd(J.)30 b(Stat.)g(Phys.)f Fs(86)e Ft(581-673)42 556 y([6])41 b(Vilenkin)33 b(N)g(J)f(1968)e Fd(Sp)l(e)l(cial)36 b(F)-6 b(unctions)33 b(and)i(the)g(The)l(ory)g(of)h (Gr)l(oup)e(R)l(epr)l(esentations)f Ft(\(Pro)n(vidence,)f(RI:)254 664 y(American)27 b(Mathematical)g(So)r(ciet)n(y\))42 772 y([7])41 b(See)27 b(page)g(472)f(equation)h(\(3\))h(of)f (Vilenkin's)h(b)r(o)r(ok)g([6)o(])42 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3790 1063 4 v 668 3856 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 3826 y Fl(3)923 3856 y Fo(n)966 3837 y Fl(3)1033 3856 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+4\))1441 3826 y Fl(3)1508 3856 y Fn(\()p Fo(n)p Fn(+6\))1696 3826 y Fl(3)2105 3766 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 3742 y Fl(3)2656 3766 y Fn(\()p Fo(n)p Fn(+1\))p 2105 3790 739 4 v 2236 3847 a(6)f(\()p Fo(n)p Fn(+4\))g(\()p Fo(n)p Fn(+6\))0 4009 y Fq(\(1)f(3)h(4)f(2)g(4)g(3\))890 3962 y Fn(20736)i(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fn(+2\))p 668 3986 1063 4 v 668 4052 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 4022 y Fl(4)923 4052 y Fo(n)966 4033 y Fl(3)1033 4052 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+4\))1441 4022 y Fl(3)1508 4052 y Fn(\()p Fo(n)p Fn(+6\))1696 4022 y Fl(3)2105 3962 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 3938 y Fl(2)2656 3962 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+2\))3064 3932 y Fl(2)p 2105 3986 994 4 v 2364 4043 a Fn(2)g(\()p Fo(n)p Fn(+4\))g(\()p Fo(n)p Fn(+6\))0 4199 y Fq(\(1)f(3)h(4)f(3)g(3)g (4\))1111 4152 y Fn(62208)i(\()p Fo(n)p Fk(\000)p Fn(2\))p 668 4176 1284 4 v 668 4242 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 4212 y Fl(4)923 4242 y Fo(n)966 4223 y Fl(2)1033 4242 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+4\))1441 4212 y Fl(3)1508 4242 y Fn(\()p Fo(n)p Fn(+6\))1696 4212 y Fl(3)1763 4242 y Fn(\()p Fo(n)p Fn(+8\))2105 4152 y(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 4128 y Fl(4)2656 4152 y Fn(\()p Fo(n)p Fn(+1\))p 2105 4176 739 4 v 2236 4234 a(2)f(\()p Fo(n)p Fn(+6\))g(\()p Fo(n)p Fn(+8\))0 4389 y Fq(\(1)f(3)h(4)f(4)g(4)g(3\))1000 4342 y Fn(124416)j(\()p Fo(n)p Fk(\000)p Fn(2\))e(\()p Fo(n)p Fn(+3\))p 668 4366 1318 4 v 668 4432 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 4403 y Fl(4)923 4432 y Fo(n)966 4413 y Fl(2)1033 4432 y Fn(\()p Fo(n)p Fn(+1\))1220 4403 y Fl(2)1288 4432 y Fn(\()p Fo(n)p Fn(+4\))1475 4403 y Fl(3)1543 4432 y Fn(\()p Fo(n)p Fn(+6\))1730 4403 y Fl(3)1798 4432 y Fn(\()p Fo(n)p Fn(+8\))2105 4342 y(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 4318 y Fl(4)2656 4342 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+3\))p 2105 4366 959 4 v 2346 4424 a(4)g(\()p Fo(n)p Fn(+4\))h(\()p Fo(n)p Fn(+8\))0 4585 y Fq(\(2)e(2)h(2)f(2)g(2)g (2\))677 4538 y Fn(64)h(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)1070 4514 y Fl(2)1105 4538 y Fn(+4)p Fo(n)p Fk(\000)p Fn(24\))p 668 4562 733 4 v 668 4628 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 4598 y Fl(5)923 4628 y Fn(\()p Fo(n)p Fn(+2\))1111 4598 y Fl(3)1178 4628 y Fn(\()p Fo(n)p Fn(+4\))1366 4598 y Fl(3)2105 4538 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h(\()p Fo(n)p Fn(+2\))2734 4509 y Fl(3)2801 4538 y Fn(\()p Fo(n)2871 4514 y Fl(2)2906 4538 y Fn(+4)p Fo(n)p Fk(\000)p Fn(24\))p 2105 4562 1087 4 v 2537 4628 a(\()p Fo(n)p Fn(+4\))2725 4598 y Fl(3)0 4781 y Fq(\(2)e(2)h(2)f(2)g(2)g(4\))943 4734 y Fn(768)i(\()p Fo(n)p Fk(\000)p Fn(2\))f Fo(n)p 668 4758 953 4 v 668 4824 a Fn(\()p Fo(n)p Fk(\000)p Fn(1\))856 4794 y Fl(5)923 4824 y Fn(\()p Fo(n)p Fn(+2\))1111 4794 y Fl(3)1178 4824 y Fn(\()p Fo(n)p Fn(+4\))1366 4794 y Fl(3)1433 4824 y Fn(\()p Fo(n)p Fn(+6\))2105 4734 y(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 4710 y Fl(2)2656 4734 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+2\))3064 4704 y Fl(2)p 2105 4758 994 4 v 2491 4824 a Fn(\()p Fo(n)p Fn(+4\))2678 4794 y Fl(3)0 4977 y Fq(\(2)f(2)h(2)f(2)g (4)g(4\))1074 4930 y Fn(4608)h(\()p Fo(n)p Fk(\000)p Fn(2\))p 668 4954 1174 4 v 668 5020 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 4990 y Fl(5)923 5020 y Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+2\))g(\()p Fo(n)p Fn(+4\))1551 4990 y Fl(3)1618 5020 y Fn(\()p Fo(n)p Fn(+6\))1806 4990 y Fl(2)2105 4930 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)2589 4906 y Fl(2)2656 4930 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+2\))3064 4900 y Fl(3)p 2105 4954 994 4 v 2457 5020 a Fn(2)f(\()p Fo(n)p Fn(+4\))2712 4990 y Fl(3)p 0 5070 3252 9 v eop %%Page: 8 8 8 7 bop 0 17 a Fh(Coupling)34 b(c)-5 b(o)g(e\016cients)34 b(of)g(SO\(n\))2370 b Fq(8)598 274 y Fs(T)-8 b(able)32 b(1.)k Fd(c)l(ont.)p 0 315 3039 9 v 0 433 a Fq(\()p Fp(`)79 448 y Fn(1)118 433 y Fp(`)159 448 y Fn(2)199 433 y Fp(`)240 448 y Fn(3)279 433 y Fp(`)320 448 y Fn(4)359 433 y Fp(`)400 448 y Fn(5)440 433 y Fp(`)481 448 y Fn(6)520 433 y Fq(\))100 b Fp(I)701 448 y Fo(n)748 433 y Fq(\()p Fp(`)827 448 y Fn(1)866 433 y Fp(;)17 b(`)951 448 y Fn(2)990 433 y Fp(;)g(`)1075 448 y Fn(3)1114 433 y Fu(j)p Fp(`)1183 448 y Fn(4)1222 433 y Fp(;)g(`)1307 448 y Fn(5)1346 433 y Fp(;)g(`)1431 448 y Fn(6)1470 433 y Fq(\))p 0 501 3039 4 v 0 629 a(\(2)32 b(2)h(2)f(3)g(3)g(3\))668 581 y Fn(864)h(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)1317 558 y Fl(3)1352 581 y Fn(+8)p Fo(n)1485 558 y Fl(2)1519 581 y Fk(\000)p Fn(28)p Fo(n)p Fk(\000)p Fn(48\))p 668 606 1173 4 v 705 671 a(\()p Fo(n)p Fk(\000)p Fn(1\))893 642 y Fl(5)960 671 y Fo(n)1003 652 y Fl(2)1070 671 y Fn(\()p Fo(n)p Fn(+2\))1258 642 y Fl(3)1325 671 y Fn(\()p Fo(n)p Fn(+4\))1513 642 y Fl(3)1580 671 y Fn(\()p Fo(n)p Fn(+6\))1768 642 y Fl(2)0 819 y Fq(\(2)e(2)h(2)f(4)g(4)g(4\))797 772 y Fn(18432)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\()p Fo(n)1296 748 y Fl(3)1331 772 y Fn(+12)p Fo(n)1499 748 y Fl(2)1534 772 y Fk(\000)p Fn(24)p Fo(n)p Fk(\000)p Fn(128\))p 668 796 1353 4 v 668 862 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 832 y Fl(5)923 862 y Fo(n)966 843 y Fl(2)1033 862 y Fn(\()p Fo(n)p Fn(+1\))1220 832 y Fl(2)1288 862 y Fn(\()p Fo(n)p Fn(+4\))1475 832 y Fl(3)1543 862 y Fn(\()p Fo(n)p Fn(+6\))1730 832 y Fl(2)1798 862 y Fn(\()p Fo(n)p Fn(+8\))1985 832 y Fl(2)0 1009 y Fq(\(2)f(2)h(4)f(2)g(2)g(4\))1036 962 y Fn(2304)i(\()p Fo(n)p Fk(\000)p Fn(2\))f Fo(n)1473 938 y Fl(2)p 668 986 1208 4 v 668 1052 a Fn(\()p Fo(n)p Fk(\000)p Fn(1\))856 1022 y Fl(5)923 1052 y Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+2\))1331 1022 y Fl(3)1398 1052 y Fn(\()p Fo(n)p Fn(+4\))1586 1022 y Fl(3)1653 1052 y Fn(\()p Fo(n)p Fn(+6\))1841 1022 y Fl(3)0 1194 y Fq(\(2)f(2)h(4)f(2)g (4)g(4\))1073 1146 y Fn(55296)i(\()p Fo(n)p Fk(\000)p Fn(2\))p 668 1171 V 668 1236 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 1207 y Fl(5)923 1236 y Fn(\()p Fo(n)p Fn(+1\))1111 1207 y Fl(2)1178 1236 y Fn(\()p Fo(n)p Fn(+4\))1366 1207 y Fl(3)1433 1236 y Fn(\()p Fo(n)p Fn(+6\))1621 1207 y Fl(3)1688 1236 y Fn(\()p Fo(n)p Fn(+8\))0 1378 y Fq(\(2)e(2)h(4)f(3)g (3)g(3\))963 1330 y Fn(20736)i(\()p Fo(n)p Fk(\000)p Fn(2\))p 668 1355 988 4 v 668 1420 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 1391 y Fl(5)923 1420 y Fn(\()p Fo(n)p Fn(+2\))1111 1391 y Fl(2)1178 1420 y Fn(\()p Fo(n)p Fn(+4\))1366 1391 y Fl(3)1433 1420 y Fn(\()p Fo(n)p Fn(+6\))1621 1391 y Fl(3)0 1562 y Fq(\(2)e(2)h(4)f(4)g(4)g(2\))943 1515 y Fn(13824)i(\()p Fo(n)p Fk(\000)p Fn(2\))f Fo(n)f Fn(\()p Fo(n)p Fn(+3\))p 668 1539 1243 4 v 668 1605 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 1576 y Fl(5)923 1605 y Fn(\()p Fo(n)p Fn(+1\))1111 1576 y Fl(2)1178 1605 y Fn(\()p Fo(n)p Fn(+2\))1366 1576 y Fl(2)1433 1605 y Fn(\()p Fo(n)p Fn(+4\))1621 1576 y Fl(3)1688 1605 y Fn(\()p Fo(n)p Fn(+6\))1876 1576 y Fl(3)0 1747 y Fq(\(2)g(2)h(4)f(4)g(4)g(4\))963 1699 y Fn(663552)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\()p Fo(n)p Fn(+3\))p 668 1724 V 668 1789 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 1760 y Fl(5)923 1789 y Fn(\()p Fo(n)p Fn(+1\))1111 1760 y Fl(3)1178 1789 y Fn(\()p Fo(n)p Fn(+4\))1366 1760 y Fl(3)1433 1789 y Fn(\()p Fo(n)p Fn(+6\))1621 1760 y Fl(3)1688 1789 y Fn(\()p Fo(n)p Fn(+8\))1876 1760 y Fl(2)0 1937 y Fq(\(2)f(3)h(3)f(2)g(3)g(3\))668 1889 y Fn(2592)h(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fn(+1\))f(\(2)p Fo(n)1387 1866 y Fl(4)1422 1889 y Fn(+17)p Fo(n)1590 1866 y Fl(3)1625 1889 y Fk(\000)p Fn(14)p Fo(n)1793 1866 y Fl(2)1828 1889 y Fk(\000)p Fn(84)p Fo(n)p Fk(\000)p Fn(72\))p 668 1914 1482 4 v 860 1979 a(\()p Fo(n)p Fk(\000)p Fn(1\))1048 1950 y Fl(5)1115 1979 y Fo(n)1158 1960 y Fl(3)1225 1979 y Fn(\()p Fo(n)p Fn(+2\))1413 1950 y Fl(3)1480 1979 y Fn(\()p Fo(n)p Fn(+4\))1668 1950 y Fl(3)1735 1979 y Fn(\()p Fo(n)p Fn(+6\))1923 1950 y Fl(3)0 2127 y Fq(\(2)f(3)h(3)f(3)g (4)g(4\))780 2080 y Fn(124416)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\()p Fo(n)1314 2056 y Fl(3)1349 2080 y Fn(+10)p Fo(n)1517 2056 y Fl(2)1552 2080 y Fk(\000)p Fn(20)p Fo(n)p Fk(\000)p Fn(48\))p 668 2104 1318 4 v 668 2169 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 2140 y Fl(5)923 2169 y Fo(n)966 2151 y Fl(3)1033 2169 y Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+4\))1441 2140 y Fl(3)1508 2169 y Fn(\()p Fo(n)p Fn(+6\))1696 2140 y Fl(3)1763 2169 y Fn(\()p Fo(n)p Fn(+8\))1951 2140 y Fl(2)0 2317 y Fq(\(2)f(3)h(3)f(4)g(3)g(3\))780 2270 y Fn(15552)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\()p Fo(n)1279 2246 y Fl(3)1314 2270 y Fn(+11)p Fo(n)1482 2246 y Fl(2)1517 2270 y Fk(\000)p Fn(48)p Fo(n)p Fk(\000)p Fn(36\))p 668 2294 1284 4 v 668 2360 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 2330 y Fl(5)923 2360 y Fo(n)966 2341 y Fl(3)1033 2360 y Fn(\()p Fo(n)p Fn(+2\))g(\()p Fo(n)p Fn(+4\))1441 2330 y Fl(3)1508 2360 y Fn(\()p Fo(n)p Fn(+6\))1696 2330 y Fl(3)1763 2360 y Fn(\()p Fo(n)p Fn(+8\))0 2507 y Fq(\(2)f(4)h(4)f(2)g (4)g(4\))668 2460 y Fn(221184)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\()p Fo(n)p Fn(+2\))h(\(3)p Fo(n)1458 2436 y Fl(4)1493 2460 y Fn(+40)p Fo(n)1661 2436 y Fl(3)1696 2460 y Fn(+72)p Fo(n)1864 2436 y Fl(2)1899 2460 y Fk(\000)p Fn(192)p Fo(n)p Fk(\000)p Fn(512\))p 668 2484 1623 4 v 803 2550 a(\()p Fo(n)p Fk(\000)p Fn(1\))991 2520 y Fl(5)1058 2550 y Fo(n)1101 2531 y Fl(3)1168 2550 y Fn(\()p Fo(n)p Fn(+1\))1356 2520 y Fl(3)1423 2550 y Fn(\()p Fo(n)p Fn(+4\))1611 2520 y Fl(3)1678 2550 y Fn(\()p Fo(n)p Fn(+6\))1866 2520 y Fl(3)1933 2550 y Fn(\()p Fo(n)p Fn(+8\))2121 2520 y Fl(3)0 2697 y Fq(\(2)e(4)h(4)f(4)g(4)g(4\))669 2650 y Fn(3981312)j(\()p Fo(n)p Fk(\000)p Fn(2\))e(\()p Fo(n)p Fn(+2\))h(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)1680 2626 y Fl(3)1715 2650 y Fn(+14)p Fo(n)1883 2626 y Fl(2)1918 2650 y Fk(\000)p Fn(16)p Fo(n)p Fk(\000)p Fn(128\))p 668 2674 1609 4 v 668 2740 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 2711 y Fl(5)923 2740 y Fo(n)966 2721 y Fl(2)1033 2740 y Fn(\()p Fo(n)p Fn(+1\))1220 2711 y Fl(4)1288 2740 y Fn(\()p Fo(n)p Fn(+4\))1475 2711 y Fl(3)1543 2740 y Fn(\()p Fo(n)p Fn(+6\))1730 2711 y Fl(3)1798 2740 y Fn(\()p Fo(n)p Fn(+8\))1985 2711 y Fl(3)2053 2740 y Fn(\()p Fo(n)p Fn(+10\))0 2888 y Fq(\(3)f(3)h(4)f(3)g(3)g(4\))864 2840 y Fn(186624)i(\()p Fo(n)p Fk(\000)p Fn(2\))f(\(4)p Fo(n)1433 2817 y Fl(2)1468 2840 y Fn(+37)p Fo(n)p Fk(\000)p Fn(50\))p 668 2865 1318 4 v 668 2930 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 2901 y Fl(5)923 2930 y Fo(n)966 2911 y Fl(2)1033 2930 y Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+4\))1441 2901 y Fl(3)1508 2930 y Fn(\()p Fo(n)p Fn(+6\))1696 2901 y Fl(3)1763 2930 y Fn(\()p Fo(n)p Fn(+8\))1951 2901 y Fl(3)0 3072 y Fq(\(3)f(3)h(4)f(4)g (4)g(3\))780 3024 y Fn(373248)i(\()p Fo(n)p Fk(\000)p Fn(4\))f(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)p Fn(+20\))p 668 3049 1353 4 v 668 3114 a(\()p Fo(n)p Fk(\000)p Fn(1\))856 3085 y Fl(5)923 3114 y Fo(n)966 3095 y Fl(2)1033 3114 y Fn(\()p Fo(n)p Fn(+1\))1220 3085 y Fl(2)1288 3114 y Fn(\()p Fo(n)p Fn(+4\))1475 3085 y Fl(3)1543 3114 y Fn(\()p Fo(n)p Fn(+6\))1730 3085 y Fl(3)1798 3114 y Fn(\()p Fo(n)p Fn(+8\))1985 3085 y Fl(3)0 3262 y Fq(\(4)f(4)h(4)f(4)g(4)g(4\))668 3215 y Fn(11943936)i(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)1493 3191 y Fl(6)1528 3215 y Fn(+43)p Fo(n)1696 3191 y Fl(5)1731 3215 y Fn(+400)p Fo(n)1934 3191 y Fl(4)1969 3215 y Fk(\000)p Fn(212)p Fo(n)2172 3191 y Fl(3)2207 3215 y Fk(\000)p Fn(6752)p Fo(n)2445 3191 y Fl(2)2481 3215 y Fk(\000)p Fn(5888)p Fo(n)p Fn(+15360\))p 668 3239 2311 4 v 1002 3304 a(\()p Fo(n)p Fk(\000)p Fn(1\))1190 3275 y Fl(5)1257 3304 y Fo(n)1300 3286 y Fl(2)1367 3304 y Fn(\()p Fo(n)p Fn(+1\))1554 3275 y Fl(5)1622 3304 y Fn(\()p Fo(n)p Fn(+4\))1809 3275 y Fl(3)1877 3304 y Fn(\()p Fo(n)p Fn(+6\))2064 3275 y Fl(3)2132 3304 y Fn(\()p Fo(n)p Fn(+8\))2319 3275 y Fl(3)2387 3304 y Fn(\()p Fo(n)p Fn(+10\))2610 3275 y Fl(3)p 0 3354 3039 9 v eop %%Page: 9 9 9 8 bop 0 17 a Fh(Coupling)34 b(c)-5 b(o)g(e\016cients)34 b(of)g(SO\(n\))2370 b Fq(9)598 274 y Fs(T)-8 b(able)32 b(1.)k Fd(c)l(ont.)p 0 315 3530 9 v 0 441 a Fq(\()p Fp(`)79 456 y Fn(1)118 441 y Fp(`)159 456 y Fn(2)199 441 y Fp(`)240 456 y Fn(3)279 441 y Fp(`)320 456 y Fn(4)359 441 y Fp(`)400 456 y Fn(5)440 441 y Fp(`)481 456 y Fn(6)520 441 y Fq(\))100 b Fp(c)700 390 y Fn(\()p Fo(\013)p Fn(\))700 468 y Fo(`)729 477 y Fl(1)763 468 y Fo(`)792 477 y Fl(2)827 468 y Fo(`)856 477 y Fl(3)890 468 y Fo(`)919 477 y Fl(4)953 468 y Fo(`)982 477 y Fl(5)1017 468 y Fo(`)1046 477 y Fl(6)p 0 509 3530 4 v 0 637 a Fq(\(2)32 b(2)h(2)f(3)g(3)g(3\))668 589 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)g Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)1474 566 y Fl(3)1509 589 y Fn(+8)p Fo(n)1642 566 y Fl(2)1677 589 y Fk(\000)p Fn(28)p Fo(n)p Fk(\000)p Fn(48\))p 668 614 1331 4 v 1188 679 a(2)f(\()p Fo(n)p Fn(+6\))1443 650 y Fl(2)0 833 y Fq(\(2)g(2)h(2)f(4)g(4)g(4\))668 785 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)g Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+2\))1592 756 y Fl(3)1659 785 y Fn(\()p Fo(n)p Fn(+6\))h(\()p Fo(n)1950 762 y Fl(3)1984 785 y Fn(+12)p Fo(n)2152 762 y Fl(2)2187 785 y Fk(\000)p Fn(24)p Fo(n)p Fk(\000)p Fn(128\))p 668 810 1877 4 v 1333 875 a(6)f(\()p Fo(n)p Fn(+4\))1589 846 y Fl(3)1656 875 y Fn(\()p Fo(n)p Fn(+8\))1844 846 y Fl(2)0 1023 y Fq(\(2)f(2)h(4)f(2)g(2)g(4\))668 975 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 952 y Fl(4)1218 975 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))p 668 1000 959 4 v 892 1065 a(4)f(\()p Fo(n)p Fn(+4\))1148 1036 y Fl(3)1215 1065 y Fn(\()p Fo(n)p Fn(+6\))0 1219 y Fq(\(2)f(2)h(4)f(2)g(4)g(4\))668 1171 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 1148 y Fl(3)1218 1171 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))1627 1142 y Fl(3)p 668 1196 994 4 v 909 1261 a Fn(2)f(\()p Fo(n)p Fn(+4\))1165 1232 y Fl(3)1232 1261 y Fn(\()p Fo(n)p Fn(+8\))0 1409 y Fq(\(2)f(2)h(4)f(3)g(3)g(3\))668 1361 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 1338 y Fl(4)1218 1361 y Fn(\()p Fo(n)p Fn(+1\))p 668 1386 739 4 v 926 1451 a(\()p Fo(n)p Fn(+6\))1114 1422 y Fl(2)0 1599 y Fq(\(2)f(2)h(4)f(4)g(4)g(2\))668 1552 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 1528 y Fl(4)1218 1552 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))f(\()p Fo(n)p Fn(+3\))p 668 1576 1180 4 v 1112 1641 a(8)g(\()p Fo(n)p Fn(+4\))1368 1612 y Fl(3)0 1795 y Fq(\(2)f(2)h(4)f(4)g(4)g(4\))668 1747 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 1724 y Fl(4)1218 1747 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))1627 1718 y Fl(2)1694 1747 y Fn(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)p Fn(+6\))p 668 1772 1435 4 v 1112 1837 a(2)g(\()p Fo(n)p Fn(+4\))1368 1808 y Fl(3)1435 1837 y Fn(\()p Fo(n)p Fn(+8\))1623 1808 y Fl(2)0 1985 y Fq(\(2)f(3)h(3)f(2)g(3)g(3\))668 1938 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)g Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+4\))h(\(2)p Fo(n)1730 1914 y Fl(4)1765 1938 y Fn(+17)p Fo(n)1933 1914 y Fl(3)1968 1938 y Fk(\000)p Fn(14)p Fo(n)2136 1914 y Fl(2)2170 1938 y Fk(\000)p Fn(84)p Fo(n)p Fk(\000)p Fn(72\))p 668 1962 1824 4 v 1324 2028 a(2)f(\()p Fo(n)p Fn(+2\))h(\()p Fo(n)p Fn(+6\))1800 1998 y Fl(3)0 2175 y Fq(\(2)e(3)h(3)f(3)g(4)g(4\))668 2128 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 2104 y Fl(2)1218 2128 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))f(\()p Fo(n)1729 2104 y Fl(3)1764 2128 y Fn(+10)p Fo(n)1932 2104 y Fl(2)1967 2128 y Fk(\000)p Fn(20)p Fo(n)p Fk(\000)p Fn(48\))p 668 2152 1621 4 v 1223 2218 a(2)f(\()p Fo(n)p Fn(+6\))i(\()p Fo(n)p Fn(+8\))1699 2188 y Fl(2)0 2365 y Fq(\(2)e(3)h(3)f(4)g(3)g(3\)) 668 2318 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 2294 y Fl(2)1218 2318 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+4\))f(\()p Fo(n)1729 2294 y Fl(3)1764 2318 y Fn(+11)p Fo(n)1932 2294 y Fl(2)1967 2318 y Fk(\000)p Fn(48)p Fo(n)p Fk(\000)p Fn(36\))p 668 2342 V 1223 2408 a(4)f(\()p Fo(n)p Fn(+6\))1478 2379 y Fl(2)1545 2408 y Fn(\()p Fo(n)p Fn(+8\))0 2561 y Fq(\(2)g(4)h(4)f(2)g (4)g(4\))668 2514 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)g Fn(\()p Fo(n)p Fn(+1\))g(\()p Fo(n)p Fn(+2\))1592 2485 y Fl(3)1659 2514 y Fn(\()p Fo(n)p Fn(+6\))h(\(3)p Fo(n)1985 2490 y Fl(4)2020 2514 y Fn(+40)p Fo(n)2188 2490 y Fl(3)2223 2514 y Fn(+72)p Fo(n)2391 2490 y Fl(2)2425 2514 y Fk(\000)p Fn(192)p Fo(n)p Fk(\000)p Fn(512\))p 668 2538 2150 4 v 1470 2604 a(6)f(\()p Fo(n)p Fn(+4\))1725 2574 y Fl(3)1793 2604 y Fn(\()p Fo(n)p Fn(+8\))1980 2574 y Fl(3)0 2757 y Fq(\(2)f(4)h(4)f(4)g(4)g(4\))668 2710 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 2686 y Fl(3)1218 2710 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+2\))1627 2681 y Fl(2)1694 2710 y Fn(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)p Fn(+6\))2102 2681 y Fl(2)2169 2710 y Fn(\()p Fo(n)2239 2686 y Fl(3)2274 2710 y Fn(+14)p Fo(n)2442 2686 y Fl(2)2477 2710 y Fk(\000)p Fn(16)p Fo(n)p Fk(\000)p Fn(128\))p 668 2734 2166 4 v 1350 2800 a(4)g(\()p Fo(n)p Fn(+4\))1606 2770 y Fl(3)1673 2800 y Fn(\()p Fo(n)p Fn(+8\))1861 2770 y Fl(3)1928 2800 y Fn(\()p Fo(n)p Fn(+10\))0 2947 y Fq(\(3)f(3)h(4)f(3) g(3)g(4\))668 2900 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 2876 y Fl(4)1218 2900 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+4\))f(\(4)p Fo(n)1764 2876 y Fl(2)1799 2900 y Fn(+37)p Fo(n)p Fk(\000)p Fn(50\))p 668 2925 1453 4 v 1139 2990 a(4)g(\()p Fo(n)p Fn(+6\))g(\()p Fo(n)p Fn(+8\))1615 2961 y Fl(3)0 3138 y Fq(\(3)f(3)h(4)f(4)g(4)g(3\))668 3090 y Fn(\()p Fo(n)p Fk(\000)p Fn(4\))h(\()p Fo(n)p Fk(\000)p Fn(2\))g(\()p Fo(n)p Fk(\000)p Fn(1\))h Fo(n)1372 3067 y Fl(4)1439 3090 y Fn(\()p Fo(n)p Fn(+1\))f(\()p Fo(n)p Fn(+3\))h(\()p Fo(n)p Fn(+20\))p 668 3115 1436 4 v 1240 3180 a(8)f(\()p Fo(n)p Fn(+8\))1496 3151 y Fl(3)0 3334 y Fq(\(4)f(4)h(4)f(4)g(4)g(4\)) 668 3286 y Fn(\()p Fo(n)p Fk(\000)p Fn(2\))h(\()p Fo(n)p Fk(\000)p Fn(1\))g Fo(n)1151 3263 y Fl(4)1218 3286 y Fn(\()p Fo(n)p Fn(+1\))h(\()p Fo(n)p Fn(+3\))f(\()p Fo(n)p Fn(+6\))1847 3257 y Fl(3)1914 3286 y Fn(\()p Fo(n)1984 3263 y Fl(6)2019 3286 y Fn(+43)p Fo(n)2187 3263 y Fl(5)2222 3286 y Fn(+400)p Fo(n)2425 3263 y Fl(4)2460 3286 y Fk(\000)p Fn(212)p Fo(n)2663 3263 y Fl(3)2698 3286 y Fk(\000)p Fn(6752)p Fo(n)2936 3263 y Fl(2)2972 3286 y Fk(\000)p Fn(5888)p Fo(n)p Fn(+15360\))p 668 3311 2802 4 v 1633 3376 a(16)g(\()p Fo(n)p Fn(+4\))1924 3347 y Fl(3)1991 3376 y Fn(\()p Fo(n)p Fn(+8\))2179 3347 y Fl(3)2246 3376 y Fn(\()p Fo(n)p Fn(+10\))2469 3347 y Fl(3)p 0 3454 3530 9 v eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------9903190313174--