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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
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
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
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Feb 13 2013
STATUS
approved