The On-Line Encyclopedia of Integer Sequences (OEIS)

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A319145

E.g.f. A = A(x,m) satisfies: cn(A + x, m) + sn(A - x, m) = 1, where sn(x,m) and cn(x,m) are Jacobi elliptic functions with parameter m, as an irregular triangle of coefficients read by rows.
(history; published version)

#16 by Paul D. Hanna at Thu Sep 13 16:18:45 EDT 2018

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approved

#15 by Paul D. Hanna at Thu Sep 13 16:18:42 EDT 2018

PROG

S = intformal(C*D +x*O(x^21n));

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#14 by Paul D. Hanna at Wed Sep 12 17:27:53 EDT 2018

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#13 by Paul D. Hanna at Wed Sep 12 17:27:51 EDT 2018

LINKS

Paul D. Hanna, <a href="/A319145/b319145.txt">Table of n, a(n) for n = 1..930, for rows 1..60 of this triangle in flattened form.</a>

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approved

editing

#12 by Paul D. Hanna at Wed Sep 12 17:26:16 EDT 2018

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approved

#11 by Paul D. Hanna at Wed Sep 12 17:26:14 EDT 2018

NAME

E.g.f. A = A(x,m) satisfies: cn(A + x, m) + sn(A - x, m) = 1, where sn(x,m) and cn(x,m) are Jacobi elliptic functions with parameter m, as an irregular triangle of coefficients read by rows.

LINKS

Paul D. Hanna, <a href="/A319145/b319145.txt">Table of n, a(n) for n = 1..930</a>

CROSSREFS

Cf. A318005 (column 0).

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#10 by Paul D. Hanna at Wed Sep 12 09:25:21 EDT 2018

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#9 by Paul D. Hanna at Wed Sep 12 09:25:18 EDT 2018

KEYWORD

sign,tabf,new

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#8 by Paul D. Hanna at Wed Sep 12 09:24:58 EDT 2018

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#7 by Paul D. Hanna at Wed Sep 12 09:24:56 EDT 2018

EXAMPLE

(cn(A) + sn(A)*dn(x))/sqrt(1 - m*sn(x)^2*sn(A)^2) = 1 + x + 3*x^2/2! + (-4*m + 11)*x^3/3! + (-96*m + 57)*x^4/4! + (16*m^2 - 1816*m + 361)*x^5/5! + (3168*m^2 - 34848*m + 2763)*x^6/6! + (-64*m^3 + 204720*m^2 - 722220*m + 24611)*x^7/7! + (-109056*m^3 + 9767808*m^2 - 16653888*m + 250737)*x^8/8! + (256*m^4 - 20794112*m^3 + 420953568*m^2 - 433038512*m + 2873041)*x^9/9! + ...

(cn(x) - sn(x)*dn(A))/sqrt(1 - m*sn(x)^2*sn(A)^2) = 1 - x - x^2/2! + (4*m + 1)*x^3/3! + (64*m + 1)*x^4/4! + (-16*m^2 + 856*m - 1)*x^5/5! + (-2656*m^2 + 13696*m - 1)*x^6/6! + (64*m^3 - 140208*m^2 + 261228*m + 1)*x^7/7! + (100864*m^3 - 5659008*m^2 + 5904768*m + 1)*x^8/8! + (-256*m^4 + 16616192*m^3 - 215989728*m^2 + 156299312*m - 1)*x^9/9! + ...

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approved

editing