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

```

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