The On-Line Encyclopedia of Integer Sequences (OEIS)

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A193826

Expansion of psi(x^2) * phi(x^7) / (f(-x) * f(-x^7)) in powers of x where phi(), psi(), f() are Ramanujan theta functions.
(history; published version)

#22 by Charles R Greathouse IV at Fri Mar 12 22:24:46 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

#21 by N. J. A. Sloane at Wed Nov 13 22:00:12 EST 2019

LINKS

M. Somos, <a href="http://somos.crg4.comA010815/multiqa010815.pdftxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

22:00

OEIS Server: https://oeis.org/edit/global/2833

#20 by Alois P. Heinz at Thu Jul 26 07:43:42 EDT 2018

STATUS

reviewed

approved

#19 by Michel Marcus at Wed Jul 25 23:50:55 EDT 2018

STATUS

proposed

reviewed

#18 by G. C. Greubel at Wed Jul 25 21:13:32 EDT 2018

STATUS

editing

proposed

#17 by G. C. Greubel at Wed Jul 25 21:13:13 EDT 2018

LINKS

G. C. Greubel, <a href="/A193826/b193826.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#16 by Vaclav Kotesovec at Wed Nov 15 12:15:31 EST 2017

STATUS

editing

approved

#15 by Vaclav Kotesovec at Wed Nov 15 12:15:25 EST 2017

FORMULA

a(n) ~ exp(4*Pi*sqrt(n/21)) / (2^(5/2) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017

STATUS

approved

editing

#14 by Michael Somos at Fri Apr 24 22:17:21 EDT 2015

STATUS

editing

approved

#13 by Michael Somos at Fri Apr 24 22:16:42 EDT 2015

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somos.crg4.com/multiq.pdf">Introduction to Ramanujan theta functions</a>

EXAMPLE

G.f. = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + 10*x^5 + 17*x^6 + 26*x^7 + 38*x^8 + ...

G.f. = 1/q + q^11 + 3*q^23 + 4*q^35 + 7*q^47 + 10*q^59 + 17*q^71 + 26*q^83 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] QPochhammer[ x^7, x^14] , , {x, 0, 4 n}];

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x^7] EllipticTheta[ 2, 0, x] / (2 x^(1/4) QPochhammer[ x, x] QPochhammer[ x^7, x^7]), {x, 0, n}];

a[ n_] := SeriesCoefficient[ QPochhammer[ x^14, x^28]^2 / (QPochhammer[ x, x^2] QPochhammer[ x^2, x^4]^2 QPochhammer[ x^7, x^14]^3) , , {x, 0, n}];

PROG

(PARI) {a(n) = localmy(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^14 + A)^5 / (eta(x + A) * eta(x^2 + A) * eta(x^7 + A)^3* eta(x^28 + A)^2), n))};

STATUS

approved

editing

Discussion

Fri Apr 24

22:17

Michael Somos: Light and space edits. Updated multiq URL