Re: Is there a way to integrate and differentiate Erfi?

*To*: mathgroup at smc.vnet.net*Subject*: [mg129881] Re: Is there a way to integrate and differentiate Erfi?*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Thu, 21 Feb 2013 05:46:01 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130221032829.7950068EC@smc.vnet.net>

Works fine here D[Erfi[x], x] (2*E^x^2)/Sqrt[Pi] % == Limit[(Erfi[x + d] - Erfi[x])/d, d -> 0] True Integrate[Erfi[x], x] -(E^x^2/Sqrt[Pi]) + x*Erfi[x] D[%, x] == Erfi[x] True Integrate[Erfi[x], {x, a, b}] (-a)*Erfi[a] + (E^a^2 - E^b^2 + b*Sqrt[Pi]*Erfi[b])/ Sqrt[Pi] SeriesCoefficient[Erfi[x], {x, 0, n}] Piecewise[{{2/(n*Sqrt[Pi]*((1/2)*(-1 + n))!), Mod[n, 2] == 1 && n >= 0}}, 0] The series expansion for Erfi[x] is then Sum[2/((2 n + 1) Sqrt[Pi] n!) x^(2 n + 1), {n, 0, Infinity}] Erfi[x] Integrating term-by-term Sum[2/((2 n + 1) Sqrt[Pi] n!)* Integrate[x^(2 n + 1), x], {n, 0, Infinity}] // Simplify -((-1 + E^x^2)/Sqrt[Pi]) + x*Erfi[x] Note that this differs from earlier result by an arbitrary constant of integration but its derivative is still Erfi[x] D[%, x] == Erfi[x] True Bob Hanlon On Wed, Feb 20, 2013 at 10:28 PM, <eagles.g11.teams at gmail.com> wrote: > It appears that Mathematica does not know how to integrate or differentiate the Erfi function. Am I correct? I am able to use Limit[(f(t+d)-f(t))/d, d -> 0] to get the derivative, but are there reasonable approaches to finding Integrate[Erfi]? > > Thanks! > > NS >

**References**:**Is there a way to integrate and differentiate Erfi?***From:*eagles.g11.teams@gmail.com