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 A274181 Decimal expansion of Phi(1/2, 2, 2), where Phi is the Lerch transcendent. 6
 3, 2, 8, 9, 6, 2, 1, 0, 5, 8, 6, 0, 0, 5, 0, 0, 2, 3, 6, 1, 0, 6, 2, 5, 2, 8, 0, 6, 3, 8, 7, 2, 0, 4, 3, 4, 9, 7, 6, 7, 9, 3, 8, 9, 9, 2, 2, 4, 5, 0, 5, 7, 0, 1, 7, 3, 7, 3, 8, 8, 1, 9, 1, 4, 9, 2, 6, 8, 4, 1, 7, 6, 2, 8, 6, 7, 3, 2, 8, 0, 3, 2, 6, 7, 3, 6, 1, 2, 7, 4, 3, 5, 1, 6, 6, 3, 4, 2, 8, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The exponential integral distribution is defined by p(x, m, n, mu) = ((n+mu-1)^m * x^(mu-1) / (mu-1)!) * E(x, m, n), see A163931 and the Meijer link. The moment generating function of this probability distribution function is M(a, m, n, mu) = Sum_{k>=0}(((mu+k-1)!/((mu-1)!*k!)) * ((n+mu-1) / (n+mu+k-1))^m * a^k). In the special case that mu=1 we get p(x, m, n, mu=1) = n^m * E(x, m, n) and M(a, m, n, mu=1) = n^m * Phi(a, m, n), with Phi the Lerch transcendent. If n=1 and mu=1 we get M(a, m, n=1, mu=1) = polylog(m, a)/a = Li_m(a)/a. REFERENCES William Feller, An introduction to probability theory and its applications, Vol. 1. p. 285, 1968. LINKS J. W. Meijer and N. H. G. Baken, The Exponential Integral Distribution, Statistics and Probability Letters, Volume 5, No. 3, April 1987. pp 209-211. Eric W. Weissteinâ€™s World of Mathematics, Lerch transcendent. Eric W. Weissteinâ€™s World of Mathematics, Polylogarithm. FORMULA c = Phi(1/2, 2, 2) with Phi the Lerch transcendent. c = Sum_{k>=0}(1/((2+k)^2*2^k)). c = 4 * polylog(2, 1/2) - 2. c = Pi^2/3 - 2*log(2)^2 - 2. EXAMPLE 0.32896210586005002361062528063872043497679389922... MAPLE Digits := 101; c := evalf(LerchPhi(1/2, 2, 2)); MATHEMATICA N[HurwitzLerchPhi[1/2, 2, 2], 25] (* G. C. Greubel, Jun 19 2016 *) PROG (PARI) Pi^2/3 - 2*log(2)^2 - 2 \\ Altug Alkan, Jul 08 2016 (Python) from mpmath import * mp.dps=102 print map(int, list(str(lerchphi(1/2, 2, 2))[2:-1])) # Indranil Ghosh, Jul 04 2017 CROSSREFS Cf. A163931, A002162 (Phi(1/2, 1, 1)/2), A076788 (Phi(1/2, 2, 1)/2), A112302, A008276. Sequence in context: A230432 A195305 A021308 * A195055 A214683 A060921 Adjacent sequences:  A274178 A274179 A274180 * A274182 A274183 A274184 KEYWORD cons,nonn AUTHOR Johannes W. Meijer and N. H. G. Baken, Jun 17 2016, Jul 08 2016 STATUS approved

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Last modified August 17 11:06 EDT 2019. Contains 326057 sequences. (Running on oeis4.)