how to find an expansion of: (we may assume m::posint)

(sum(a^k*b[k], k = 1 .. infinity))^m

for example: the trinomial theor...

(a+b+c)^m = sum((m,k1)*(m-k1,k2)*(m-k1-k2,k3)*c1^(k1)*c2^k2*c3^k3,k1+k2+k3=m)

here (m,k1) is the binomial coefficeitn

how to expand the following expression;

((1/6)*e*(6*(D(f))(gamma)+3*((D@@2)(f))(gamma)*e+((D@@3)(f))(gamma)*e^2))^m

i have the following transient heat conduction  equation:

dT/dt = a * d^2T/dx^2

now i have:

T(0,t ) = k1(t) : boundary condition

T(L,t) = k2(t) : boundary condtion

T(x,0) = k3(x) : initial condition

and

T(x,t) : solution at all the time

how to find out

a ?

hello friends,

how can i find analytical solution of the

dT/dt = alpha * d^2T/dx^2

T(t,x)

t: time, x: space

with maple for given temperature conditions and initial condition

sum((1/(1+2/a[k]))^(2*k+1)/(2*k+1), k = 0 .. n)

here a[k] >0, we may also assume that a[k+1] > a[k]