If and Piecewise don't quite do what I need

*To*: mathgroup at smc.vnet.net*Subject*: [mg113398] If and Piecewise don't quite do what I need*From*: Sam Takoy <sam.takoy at yahoo.com>*Date*: Wed, 27 Oct 2010 05:15:18 -0400 (EDT)

Hi, I have found that If doesn't do winside it like I would want it to do. Piecewise does do it, but then it doesn't work the way I would want it. Is there a solution that does both? Example: c[n_] := Piecewise[{{1, {n, 0}}}, Integrate[a^2 Cos[n a], {a, -Pi, Pi}]] c[n] (* Calculates the Integral *) Sum[c[n], {n, 0, Infinity}] (* But fails to Sum *) d[n_] := If[n == 0, 1, Integrate[a^2 Cos[n a], {a, -Pi, Pi}]] (* Fails to calculate the integral *) d[n] (* But does sum OK *) Sum[d[n], {n, 0, Infinity}] I want it to evaluate the integral and to sum properly. Thanks, Sam PS: Slightly offtopic, I found that the Limit trick for n = 0 with Fourier coefficients often doesn't work resulting in a 0*Infinity indetermination.