

A212186


Decimal expansion of the integral over exp(x)/sqrt(1x^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
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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 GradsteynRyzhik 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) 129132.


FORMULA

Equals Pi*(A197036+A197037)/2 .


EXAMPLE

3.104379017855555098181769863187794767228...


MATHEMATICA

RealDigits[ Pi*(BesselI[0, 1] + StruveL[0, 1])/2, 10, 107] // First (* JeanFrançois 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



