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A351401 Decimal expansion of erfi(1)/e, where erfi is the imaginary error function.

%I A351401 #19 Feb 16 2025 08:34:02
%S A351401 6,0,7,1,5,7,7,0,5,8,4,1,3,9,3,7,2,9,1,1,5,0,3,8,2,3,5,8,0,0,7,4,4,9,
%T A351401 2,1,1,6,1,2,2,0,9,2,8,6,6,5,1,5,6,9,1,5,9,1,6,9,4,4,1,9,1,9,2,7,2,0,
%U A351401 8,7,6,9,4,9,2,0,2,8,1,1,8,2,0,1,6,3,9,1,3,1,6,5,2,6,3,3,2,6,8,5,4,8,1,0,4
%N A351401 Decimal expansion of erfi(1)/e, where erfi is the imaginary error function.
%C A351401 The alternating sum of reciprocals of the factorials of the positive half-integers.
%D A351401 Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, and Sergei Rogosin, Mittag-Leffler Functions, Related Topics and Applications, New York, NY: Springer, 2020. See p. 94, eq. (4.12.9.6).
%D A351401 Constantin Milici, Gheorghe Drăgănescu, and J. Tenreiro Machado, Fractional Differential Equations, Introduction to Fractional Differential Equations, Springer, Cham, 2019. See p. 12, eq. (1.9).
%H A351401 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Erfi.html">Erfi</a>.
%H A351401 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Mittag-LefflerFunction.html">Mittag-Leffler Function</a>.
%H A351401 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mittag-Leffler_function">Mittag-Leffler function</a>.
%F A351401 Equals Sum_{k>=0} (-1)^k/(k + 1/2)! = Sum_{k>=1} (-1)^(k+1)/Gamma(k + 1/2).
%F A351401 Equals E_{1, 3/2}(-1), where E_{a,b}(z) is the two-parameter Mittag-Leffler function.
%F A351401 Equals (-1/sqrt(Pi)) * Sum_{k>=1} (-2)^k/(2*k-1)!!.
%F A351401 Equals A068985 * A099288.
%e A351401 0.60715770584139372911503823580074492116122092866515...
%p A351401 evalf(exp(-1)*erfi(1), 120);  # _Alois P. Heinz_, Feb 10 2022
%t A351401 RealDigits[Erfi[1]/E, 10, 100][[1]]
%o A351401 (PARI) real(-I*(1.0-erfc(I)))/exp(1) \\ _Michel Marcus_, Feb 10 2022
%Y A351401 Cf. A001113, A001147, A068985, A087197, A099288, A122803, A351400.
%K A351401 nonn,cons
%O A351401 0,1
%A A351401 _Amiram Eldar_, Feb 10 2022