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A121361

Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions.
(history; published version)

#9 by Charles R Greathouse IV at Fri Mar 12 22:24:44 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

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

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somos="/A010815/multiqa010815.pdftxt">Introduction to Ramanujan theta functions</a>

Discussion
Wed Nov 13	21:54	OEIS Server: https://oeis.org/edit/global/2830

#7 by Joerg Arndt at Sat Sep 16 12:01:01 EDT 2017

STATUS

proposed

approved

#6 by G. C. Greubel at Sat Sep 16 11:52:12 EDT 2017

STATUS

editing

proposed

#5 by G. C. Greubel at Sat Sep 16 11:51:25 EDT 2017

LINKS

G. C. Greubel, <a href="/A121361/b121361.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

((eta(q) * eta(q^6)) in powers of q.

STATUS

approved

editing

#4 by Michael Somos at Tue Sep 02 03:11:28 EDT 2014

STATUS

editing

approved

#3 by Michael Somos at Tue Sep 02 03:10:36 EDT 2014

	NAME	`Expansion of q^(-7/12)eta(q^2)eta(q^3)eta(q^4)eta(q^12)/(eta(q)eta(q^6)) in powers of q.` `Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions.`
	COMMENTS	`Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).`
	LINKS	`M. Somos, <a href="http://cis.csuohio.edu/~somos/multiq.pdf">Introduction to Ramanujan theta functions</a>` `Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>`
	FORMULA	`Expansion of q^(-7/12) * eta(q^2) * eta(q^3) * eta(q^4) * eta(q^12) /` `(eta(q) * eta(q^6)) in powers of q.` `2a(n) = A093829(12n + 7).`
	EXAMPLE	`G.f. = 1 + x + x^2 + x^3 + x^5 + x^6 + 2x^7 + x^8 + x^10 + x^11 + ...` `G.f. = q^7 + q^19 + q^31 + q^43 + q^67 + q^79 + 2q^91 + q^103 + ...`
	MATHEMATICA	`a[ n_] := SeriesCoefficient[ QPochhammer[ -x^1, x^6] QPochhammer[ -x^5, x^6] QPochhammer[ x^6] EllipticTheta[ 2, 0, x] / (2 x^(1/4)), {x, 0, n}]; (* Michael Somos, Sep 02 2014 *)`
	PROG	`(PARI) {a(n)=) = local(A); if(( n<0, 0, A= = x* * O(x^n); polcoeff( eta(x^2+ + A)) eta(x^3+ + A)) eta(x^4+ + A)) eta(x^12+ + A)/) / (eta(x+ + A)/) * eta(x^6+ + A), )), n))}))};`
	CROSSREFS	`Cf. A093829(12n+7)=2a(n).` `Cf. A093829.`
	STATUS	`approved` `editing`

Discussion
Tue Sep 02	03:11	Michael Somos: Added more info. Change to better NAME. Light and space edits.

#2 by Charles R Greathouse IV at Wed Apr 30 01:36:08 EDT 2014

AUTHOR

_Michael Somos, _, Jul 16 2006

Discussion
Wed Apr 30	01:36	OEIS Server: https://oeis.org/edit/global/2181

#1 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

	NAME	`Expansion of q^(-7/12)eta(q^2)eta(q^3)eta(q^4)eta(q^12)/(eta(q)eta(q^6)) in powers of q.`
	DATA	`1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 1, 3, 0, 0, 0, 1, 0, 0`
	OFFSET	`0,8`
	FORMULA	`Euler transform of period 12 sequence [ 1, 0, 0, -1, 1, 0, 1, -1, 0, 0, 1, -2, ...].`
	PROG	`(PARI) {a(n)=local(A); if(n<0, 0, A=xO(x^n); polcoeff( eta(x^2+A)eta(x^3+A)eta(x^4+A)eta(x^12+A)/eta(x+A)/eta(x^6+A), n))}`
	CROSSREFS	`Cf. A093829(12n+7)=2a(n).`
	KEYWORD	`nonn`
	AUTHOR	`Michael Somos, Jul 16 2006`
	STATUS	`approved`

Last modified August 18 19:11 EDT 2024. Contains 375273 sequences. (Running on oeis4.)