A212186 - OEIS

A212186

Decimal expansion of the integral over exp(x)/sqrt(1-x^2) dx between 0 and 1.

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

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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-François Alcover, Feb 21 2013 *)

CROSSREFS

Sequence in context: A127570 A340583 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