The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A326551 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A326551

E.g.f. C(x), where C(x*y) + i*S(x*y) = exp( i*Integral Integral C(x*y) dx dy ) such that C(x)^2 + S(x)^2 = 1.
(history; published version)

#15 by Paul D. Hanna at Sat Aug 17 12:17:05 EDT 2019

STATUS

editing

approved

#14 by Paul D. Hanna at Sat Aug 17 12:17:03 EDT 2019

COMMENTS

The e.g.f. can be derived from the functions described by A326797, A326798, and A326799.

CROSSREFS

Cf. A326797, A326798, A326799.

STATUS

approved

editing

#13 by Paul D. Hanna at Sun Jul 28 00:09:41 EDT 2019

STATUS

editing

approved

#12 by Paul D. Hanna at Sun Jul 28 00:09:39 EDT 2019

PROG

(PARI)

(PARI) {a(n) = my(C=1, S=x); for(i=1, 2*n+1, ,

S = intformal( C/x * intformal( C +x*O(x^(2*n+1)) ) );

C = 1 - intformal( S/x * intformal( C +x*O(x^(2*n+1)) ) ); ); (2*n+1)!^2*polcoeff(S, C, 2*n+1)}

CROSSREFS

Cf. A326552, A325291, A326556 (C^2).

STATUS

approved

editing

#11 by Paul D. Hanna at Sat Jul 27 21:31:29 EDT 2019

STATUS

editing

approved

#10 by Paul D. Hanna at Sat Jul 27 21:31:27 EDT 2019

COMMENTS

The e.g.f. can be derived from the functions described by A326800, A326801, and A326802.

STATUS

approved

editing

#9 by Paul D. Hanna at Sat Jul 27 21:27:41 EDT 2019

STATUS

editing

approved

#8 by Paul D. Hanna at Sat Jul 27 21:27:30 EDT 2019

CROSSREFS

Cf. A326800, A326801, A326802.

STATUS

approved

editing

#7 by Paul D. Hanna at Fri Jul 26 00:46:48 EDT 2019

STATUS

editing

approved

#6 by Paul D. Hanna at Fri Jul 26 00:46:46 EDT 2019

EXAMPLE

also, S(x*y) = sin( Integral Integral C(x*y) dx dy ).,

such that C(x)^2 + S(x)^2 = 1.

STATUS

approved

editing