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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 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: 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.)