I am new and hoping a warm welcome from this platform.
I am trying to plot the graph of double series in one variable
$$ \sum_{k=0}^{\infty} \sum_{j=0}^{\infty} C_{k,j} \exp(- 3^k 1.5^{j} x)$$
where coefficients are defined as $$ \begin{align} C_{0,0} &= 4.55672\\ C_{k,0} &= \frac{(-1)^k 3^k}{2^k \prod_{s=1}^{k}(3^s -1)}C_{0,0}\\ C_{0,j} &= \frac{(-1)^j 1.5^j}{2^j \prod_{s=1}^{j}(1.5^s-1)}C_{0,0}\\ C_{k,j} &= \frac{(-1) (3 C_{k-1,j}+1.5 C_{k,j-1})}{2(3^k 1.5^j -1)} \end{align} $$
So please tell me how to define these coefficients and can be recalled in the double sum.
Product
andSum
. Try small examples and become comfortable with these functions before tackling the big problem! Please try on your own first, based on the resources I pointed to, and then make the question specific: ask about the first speific issue you encountered. If you've never used Mathematica, then there will be a learning curve and this is too big for your very first task. $\endgroup$Product[a^s - 1, {s, k}]
gives(-1)^k QPochhammer[a, a, k]
. $\endgroup$