cp's OEIS Frontend

A053252 Coefficients of the '3rd-order' mock theta function chi(q).

%I A053252 #26 Aug 12 2023 23:00:13
%S A053252 1,1,1,0,0,0,1,1,0,0,-1,0,1,1,1,-1,0,0,0,1,0,0,-1,0,1,1,1,0,-1,-1,1,1,
%T A053252 0,-1,-1,0,1,2,1,-1,-1,0,1,1,0,-1,-2,0,1,2,1,-1,-1,-1,1,2,1,-1,-2,-1,
%U A053252 2,2,1,-1,-2,-1,1,2,0,-1,-3,0,2,3,2,-2,-2,-1,2,3,0,-2,-3,-1,2,3,2,-3,-3,-1,2,4,1,-2,-4,-1,3,4,2,-2,-4
%N A053252 Coefficients of the '3rd-order' mock theta function chi(q).
%D A053252 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 55, Eq. (26.14).
%D A053252 Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.
%D A053252 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17.
%H A053252 G. C. Greubel, <a href="/A053252/b053252.txt">Table of n, a(n) for n = 0..1000</a>
%H A053252 Leila A. Dragonette, <a href="http://dx.doi.org/10.1090/S0002-9947-1952-0049927-8">Some asymptotic formulas for the mock theta series of Ramanujan</a>, Trans. Amer. Math. Soc., 72 (1952) 474-500.
%H A053252 John F. R. Duncan, Michael J. Griffin and Ken Ono, <a href="http://arxiv.org/abs/1503.01472">Proof of the Umbral Moonshine Conjecture</a>, arXiv:1503.01472 [math.RT], 2015.
%H A053252 George N. Watson, <a href="https://doi.org/10.1112/jlms/s1-11.1.55">The final problem: an account of the mock theta functions</a>, J. London Math. Soc., 11 (1936) 55-80.
%F A053252 G.f.: chi(q) = Sum_{n >= 0} q^n^2/((1-q+q^2)*(1-q^2+q^4)*...*(1-q^n+q^(2n))).
%F A053252 G.f.: G(0), where G(k) = 1 + q^(k+1) / (1 - q^(k+1)) / G(k+1). - _Joerg Arndt_, Jun 29 2013
%t A053252 Series[Sum[q^n^2/Product[1-q^k+q^(2k), {k, 1, n}], {n, 0, 10}], {q, 0, 100}]
%Y A053252 Other '3rd-order' mock theta functions are at A000025, A053250, A053251, A053253, A053254, A053255, A261401.
%K A053252 sign,easy
%O A053252 0,38
%A A053252 _Dean Hickerson_, Dec 19 1999