A053284 Coefficients of the '10th-order' mock theta function chi(q).

0, 1, -1, 1, -2, 2, -1, 2, -3, 3, -3, 3, -4, 4, -4, 5, -6, 7, -6, 7, -9, 8, -8, 10, -12, 13, -13, 13, -16, 17, -16, 19, -21, 22, -23, 25, -28, 29, -30, 33, -37, 39, -39, 42, -48, 49, -50, 55, -60, 64, -66, 70, -77, 81, -82, 89, -97, 101, -105, 112, -121, 126, -131, 140, -151, 159, -163, 173, -187, 194, -202

Offset

0,5

References

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (corrected and extended previous b-file from G. C. Greubel)

Youn-Seo Choi, Tenth order mock theta functions in Ramanujan's lost notebook, Inventiones Mathematicae, 136 (1999) pp. 497-569.

Formula

G.f.: chi(q) = Sum_{n >= 0} (-1)^n q^(n+1)^2/((1+q)(1+q^2)...(1+q^(2n+1))).

a(n) ~ -(-1)^n * sqrt(phi) * exp(Pi*sqrt(n/10)) / (2*5^(1/4)*sqrt(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 12 2019

Mathematica

Series[Sum[(-1)^n q^(n+1)^2/Product[1+q^k, {k, 1, 2n+1}], {n, 0, 9}], {q, 0, 100}]
nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^((k+1)^2)/Product[1+x^j, {j, 1, 2*k+1}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 11 2019 *)

Crossrefs

Other '10th-order' mock theta functions are at A053281, A053282, A053283.

Sequence in context: A127830 A371275 A176816 * A050371 A172313 A022871

Adjacent sequences: A053281 A053282 A053283 * A053285 A053286 A053287

Keyword

sign,easy

Author

Dean Hickerson, Dec 19 1999

Status

approved