Re: D vs. Derivative (2)

*To*: mathgroup at smc.vnet.net*Subject*: [mg15697] Re: D vs. Derivative (2)*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Mon, 1 Feb 1999 14:54:16 -0500 (EST)*References*: <78pcjv$d3r@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Gianluca Two definitions of Derivative to avoid the problems that you found. They would need to be extended to several variables and higher derivatives, and checked out - for example for clashes of variables. With h[x_] =HypergeometricPFQ[{I,1},{1+I},x]; we got D[h[x],x] -(1/((-1 + x)*x)*I*(1 - HypergeometricPFQ[{I, 1}, {1 + I}, x] + x*HypergeometricPFQ[{I, 1}, {1 + I}, x])) but h' DirectedInfinity[((1/2 + I/2)*Sqrt[2]* Sign[Gamma[2 + I]])/Sign[Gamma[1 + I]]] & If we define Derivative[1][fn_]:= Function[ Evaluate[ Function[#, Evaluate[D[fn[#],#]] ]&[Unique[x]][#] ] ] then we get h' -(1/((-1 + #1)*#1)*I* (1 - HypergeometricPFQ[{I, 1}, {1 + I}, #1] + HypergeometricPFQ[{I, 1}, {1 + I}, #1]*#1)) & And with Derivative[1][fn_]:= Function[Evaluate[Module[{x},D[fn[x],x]/.x->#]]] we get the same: h' -(1/((-1 + #1)*#1)*I* (1 - HypergeometricPFQ[{I, 1}, {1 + I}, #1] + HypergeometricPFQ[{I, 1}, {1 + I}, #1]*#1)) & Allan, --------------------- Allan Hayes Mathematica Training and Consulting www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565