How can I do this?

*To*: mathgroup at smc.vnet.net*Subject*: [mg19090] How can I do this?*From*: "Bill Bertram" <wkb at ansto.gov.au>*Date*: Thu, 5 Aug 1999 01:35:10 -0400*Organization*: Australian Nuclear Science and Technology Organisation*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I have a problem I hope someone can help me with. I can do the following: Define an array of arbitrary length as a = Array[c,n] , where n a given integer value. I can then construct a function f[x] as an expansion in terms of known functions p[k,x] eg Legendre polynomials, as f[x_]:= Sum[a[[k]] p[k, x], {k, 1, n}]. This then gives a general function of the form f[x] = c[1] p[1, x]+c[2]p[2, x] + ...which can be formally operated upon eg by differentiation or integration. My question is, How do I go about constructing a function similar to the one above but now of two variables so that in the expansion f[t, x] = c[1] p[1, x]+c[2]p[2, x] + ... the c's are functions of t so that formal differentiations and integrations with respect to t can be carried out on it. Thanks, Bill Bertram