cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A261975 Expansion of elliptic_E / elliptic_K in powers of q.

Original entry on oeis.org

1, -8, 48, -224, 864, -2928, 9024, -25792, 69312, -176936, 432288, -1016736, 2312832, -5107504, 10983552, -23060544, 47373696, -95401872, 188637936, -366744160, 701930304, -1324016896, 2463662016, -4526174784, 8216376576, -14747939768, 26191413024, -46048199360
Offset: 0

Views

Author

Joerg Arndt, Sep 07 2015

Keywords

Links

Crossrefs

Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).
Cf. A261975 (E/K), A261977 ((E/K)^(1/2)), A261978 ((E/K)^(1/4)).
Cf. A261976 (K/E), A261979 ((K/E)^(1/2)), A261980 ((K/E)^(1/4)).

Programs

  • Mathematica
    nmax = 30; dtheta = D[Normal[Series[EllipticTheta[3, 0, x], {x, 0, nmax}]], x]; CoefficientList[Series[(EllipticTheta[4, 0, x]^4*EllipticTheta[3, 0, x] + 4*x*dtheta)/EllipticTheta[3, 0, x]^5, {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 10 2018 *)

Formula

G.f.: (T4^4 * T3 + 4*q * d/dq T3) / T3^5 where T3 = theta_3(q) and T4 = theta_4(q).

A261977 Expansion of (elliptic_E / elliptic_K)^(1/2) in powers of q.

Original entry on oeis.org

1, -4, 16, -48, 112, -248, 576, -1248, 2272, -3988, 8672, -18192, 23616, -23000, 100992, -304032, 41152, 970552, 1972816, -11299824, -9904096, 80729472, 95978688, -676487328, -755649408, 5483063076, 6371808608, -45452602080, -53224627584, 378628636264, 449486486400, -3179963494272
Offset: 0

Views

Author

Joerg Arndt, Sep 07 2015

Keywords

Crossrefs

Cf. A261975 (E/K), A261978 ((E/K)^(1/4)).
Cf. A261976 (K/E), A261979 ((K/E)^(1/2)), A261980 ((K/E)^(1/4)).
Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).

Formula

See A261975 for the g.f. for E/K.

A261978 Expansion of (elliptic_E / elliptic_K)^(1/4) in powers of q.

Original entry on oeis.org

1, -2, 6, -12, 14, -24, 84, -144, -42, 130, 1656, -3036, -9036, 17784, 76944, -147984, -591274, 1147068, 4784922, -9277164, -38983272, 75690528, 322116804, -625832880, -2687394012, 5224589254, 22613921832, -43985741688, -191670898032, 372970548504, 1634759644944, -3182191744320
Offset: 0

Views

Author

Joerg Arndt, Sep 07 2015

Keywords

Crossrefs

Cf. A261975 (E/K), A261977 ((E/K)^(1/2)).
Cf. A261976 (K/E), A261979 ((K/E)^(1/2)), A261980 ((K/E)^(1/4)).
Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).

Formula

See A261975 for the g.f. for E/K.

A261979 Expansion of (elliptic_K / elliptic_E)^(1/2) in powers of q.

Original entry on oeis.org

1, 4, 0, -16, 16, 120, -128, -928, 1056, 7572, -8960, -63408, 77248, 540504, -672000, -4665824, 5888832, 40656072, -51913728, -356835664, 459890400, 3150052992, -4090609024, -27939033312, 36509767552, 248772971228, -326815190784, -2222432164768, 2932886151552, 19910399315736
Offset: 0

Views

Author

Joerg Arndt, Sep 07 2015

Keywords

Crossrefs

Cf. A261975 (E/K), A261977 ((E/K)^(1/2)), A261978 ((E/K)^(1/4)).
Cf. A261976 (K/E), A261980 ((K/E)^(1/4)).
Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).

Formula

See A261976 for the g.f. for K/E.

A261980 Expansion of (elliptic_K / elliptic_E)^(1/4) in powers of q.

Original entry on oeis.org

1, 2, -2, -4, 14, 24, -92, -176, 694, 1342, -5480, -10612, 44532, 86408, -369328, -717616, 3109078, 6046724, -26473950, -51523620, 227477656, 442950880, -1969014572, -3835720208, 17147433572, 33415180858, -150096433272, -292574352808, 1319581377424, 2572787175656, -11644937717296
Offset: 0

Views

Author

Joerg Arndt, Sep 07 2015

Keywords

Crossrefs

Cf. A261975 (E/K), A261977 ((E/K)^(1/2)), A261978 ((E/K)^(1/4)).
Cf. A261976 (K/E), A261979 ((K/E)^(1/2)).
Cf. A004018 (elliptic K(q)), A194094 (elliptic E(q)), A115977 (elliptic k(q)^2).

Formula

See A261976 for the g.f. for K/E.

A328128 G.f.: K(4*sqrt(x)) / E(4*sqrt(x)), where E(), K() are complete elliptic integrals.

Original entry on oeis.org

1, 8, 80, 896, 10784, 136448, 1790720, 24160256, 333053504, 4670325248, 66403043840, 954931245056, 13863783325184, 202898094829568, 2989879597076480, 44320135356317696, 660370844304147584, 9884176356444627968, 148535796374189204480, 2240105752104228970496
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 04 2019

Keywords

Comments

Convolution of A002894 and A188266.

Links

Crossrefs

Cf. A002894, A188266, A261976, A328127.

Programs

  • Maple
    seq(coeff(series(EllipticK(4*sqrt(x))/EllipticE(4*sqrt(x)), x, 21), x, n), n = 0..20);
  • Mathematica
    CoefficientList[Series[EllipticK[16*x]/EllipticE[16*x], {x, 0, 20}], x]

Formula

a(n) ~ 2^(4*n-1) / n.
Showing 1-6 of 6 results.

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