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A212186 Decimal expansion of the integral over exp(x)/sqrt(1-x^2) dx between 0 and 1. 0
3, 1, 0, 4, 3, 7, 9, 0, 1, 7, 8, 5, 5, 5, 5, 5, 0, 9, 8, 1, 8, 1, 7, 6, 9, 8, 6, 3, 1, 8, 7, 7, 9, 4, 7, 6, 7, 2, 2, 8, 9, 0, 9, 2, 0, 3, 3, 6, 1, 3, 6, 8, 3, 5, 0, 9, 7, 2, 4, 8, 8, 8, 2, 6, 1, 9, 6, 8, 1, 4, 0, 3, 2, 6, 9, 9, 3, 9, 9, 9, 5, 8, 0, 2, 7, 8, 4, 6, 5, 6, 6, 3, 6, 1, 4, 8, 3, 9, 7, 6, 5, 8, 2, 8, 1, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This appears as the first integral in an attempt to expand exp(x) in a Chebyshev series between 0 and 1. Other integrals of the higher order terms in that expansion are generally bootstrapped from the lower order terms.

If we substitute x=cos(y), this is the integral over exp(cos(y)) dy from y=0 to y=Pi/2, which matches (apart from the upper limit) eq. 3.915.4 of the Gradsteyn-Ryzhik tables. - R. J. Mathar, Feb 15 2013

LINKS

Table of n, a(n) for n=1..107.

A. Karageorghis, A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function, J. Comp. Appl. Math 21 (1988) 129-132.

FORMULA

Equals Pi*(A197036+A197037)/2 .

EXAMPLE

3.104379017855555098181769863187794767228...

MATHEMATICA

RealDigits[ Pi*(BesselI[0, 1] + StruveL[0, 1])/2, 10, 107] // First (* Jean-Fran├žois Alcover, Feb 21 2013 *)

CROSSREFS

Sequence in context: A117372 A127570 A292506 * A274662 A186827 A207327

Adjacent sequences:  A212183 A212184 A212185 * A212187 A212188 A212189

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Feb 13 2013

STATUS

approved

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Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)