LINKS
M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
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Revision History for A226862
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Expansion of phi(x^3) * f(-x^4) in powers of x where phi(), f() are Ramanujan theta functions.
(history; published version)
(history; published version)
LINKS
M. Somos, <a href="http://somos.crg4.comA010815/multiqa010815.htmltxt
STATUS
editing
approved
LINKS
M. Somos, <a href="http://cis.csuohio.edu/~somos.crg4.com/multiq.pdfhtml
EXAMPLE
G.f.: = 1 + 2*x^3 - x^4 - 2*x^7 - x^8 - 2*x^11 + 2*x^12 - 2*x^16 - x^20 + 2*x^23 + ...
G.f.: = q + 2*q^19 - q^25 - 2*q^43 - q^49 - 2*q^67 + 2*q^73 - 2*q^97 - q^121 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] QPochhammer[ q^4], {q, 0, n}];
PROG
(PARI) {a(n) = localmy(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^5 / (eta(x^3 + A) * eta(x^12 + A))^2, n))};
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
G. C. Greubel, <a href="/A226862/b226862.txt">Table of n, a(n) for n = 0..2500</a>
EXAMPLE
G.f.: 1 + 2*x^3 - x^4 - 2*x^7 - x^8 - 2*x^11 + 2*x^12 - 2*x^16 - x^20 + 2*x^23 + ...
G.f.: q + 2*q^19 - q^25 - 2*q^43 - q^49 - 2*q^67 + 2*q^73 - 2*q^97 - q^121 + ...
STATUS
approved
editing
STATUS
editing
approved
FORMULA
G.f. is a period 1 Fourier series which satisfies f(-1 / (576 t)) = 384^(1/2) (t/i) g(t) where q = exp(2 pi Pi i t) and g() is the g.f. for A226861.
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed