The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A139135 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A139135

Expansion of psi(-q^3) / f(q) where psi(), f() are Ramanujan theta functions.
(history; published version)

#13 by Charles R Greathouse IV at Fri Mar 12 22:24:45 EST 2021

LINKS

M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

Discussion

Fri Mar 12

22:24

OEIS Server: https://oeis.org/edit/global/2897

#12 by N. J. A. Sloane at Wed Nov 13 21:54:13 EST 2019

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somosA010815/multiqa010815.pdftxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:54

OEIS Server: https://oeis.org/edit/global/2830

#11 by Vaclav Kotesovec at Thu Nov 16 06:14:14 EST 2017

STATUS

editing

approved

#10 by Vaclav Kotesovec at Thu Nov 16 06:14:01 EST 2017

FORMULA

a(n) ~ (-1)^n * exp(Pi*sqrt(2*n/3)) / (2^(9/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 16 2017

STATUS

approved

editing

#9 by Alois P. Heinz at Thu Oct 05 19:53:17 EDT 2017

STATUS

proposed

approved

#8 by G. C. Greubel at Thu Oct 05 19:45:02 EDT 2017

STATUS

editing

proposed

#7 by G. C. Greubel at Thu Oct 05 19:44:48 EDT 2017

LINKS

G. C. Greubel, <a href="/A139135/b139135.txt">Table of n, a(n) for n = 0..1000</a>

MATHEMATICA

A139135[n_] := SeriesCoefficient[(QPochhammer[q]* QPochhammer[q^3]*QPochhammer[q^4]*QPochhammer[q^12])/(QPochhammer[q^2]^3 *QPochhammer[q^6]), {q, 0, n}]; Table[A139135[n], {n, 0, 50}] (* G. C. Greubel, Oct 05 2017 *)

STATUS

approved

editing

#6 by Jon E. Schoenfield at Mon Oct 02 02:29:51 EDT 2017

STATUS

editing

approved

#5 by Jon E. Schoenfield at Mon Oct 02 02:29:47 EDT 2017

FORMULA

G.f. is a period 1 Fourier series which satisfies f(-1 / (108 t)) = 3^(-1/2) g(t) where q = exp(2 pi Pi i t) and g() is g.f. for A139136.

STATUS

approved

editing

#4 by Charles R Greathouse IV at Thu Mar 05 13:24:04 EST 2015

COMMENTS

Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).

Discussion

Thu Mar 05

13:24

OEIS Server: https://oeis.org/edit/global/2357