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Search: id:A115977
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| A115977 |
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Expansion of elliptic modular function lambda in powers of the nome q. |
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+0
2
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| 16, -128, 704, -3072, 11488, -38400, 117632, -335872, 904784, -2320128, 5702208, -13504512, 30952544, -68901888, 149403264, -316342272, 655445792, -1331327616, 2655115712, -5206288384, 10049485312, -19115905536, 35867019904, -66437873664
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Expansion of Jacobi elliptic m=k^2 in powers of the nome q.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 1972, p. 591.
J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 121.
A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 23.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Elliptic Lambda Function
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FORMULA
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G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^2(1-v)^2 -16v(1-u).
G.f.: 16q*(Product_{k>0} (1+q^(2k))/(1+q^(2k-1)))^8 = (theta_2(q)/theta_3(q))^4.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); 16*polcoeff( (eta(x+A)*eta(x^4+A)^2/eta(x^2+A)^3)^8, n))}
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CROSSREFS
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a(n)=16*A005798(n). a(n)=-(-1)^n*A014972(n) if n>0.
Sequence in context: A045651 A035473 A014972 this_sequence A128692 A132136 A067488
Adjacent sequences: A115974 A115975 A115976 this_sequence A115978 A115979 A115980
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 09 2006
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