The Coefficients(S, k) and Coefficients(S, [k1,.., kn]) calling sequences extract the coefficients of index k and $\left[\mathrm{k1}\,..\,\mathrm{kn}\right]$, respectively, from the series S. In these calling sequences, the dimension of the index must correspond to the dimension of S. Otherwise, an error is returned.

The Coefficients(S) calling sequence returns the general term coefficient of the series S.

$\mathrm{with}\left(\mathrm{OrthogonalSeries}\right)\:$

$S≔\mathrm{Create}\left(\frac{n+1}{m+1}\,\mathrm{GegenbauerC}\left(n\,1\,x\right)\,\mathrm{LaguerreL}\left(m\,1\,y\right)\right)$

$S≔\sum _{m=0}^{\mathrm{\infty }}\left(\sum _{n=0}^{\mathrm{\infty }}\frac{\left(n+1\right)\mathrm{GegenbauerC}\left(n\,1\,x\right)}{m+1}\right)\mathrm{LaguerreL}\left(m\,1\,y\right)$

$\mathrm{Coefficients}\left(S\right)$

$\frac{n+1}{m+1}$

$\mathrm{Coefficients}\left(S\,\left[2\,3\right]\right)$

$\frac{3}{4}$

$\mathrm{S1}≔\mathrm{Create}\left(\left[\left(1\,2\right)=4\,\left(3\,4\right)=-7\right]\,\mathrm{GegenbauerC}\left(n\,1\,x\right)\,\mathrm{LaguerreL}\left(m\,1\,y\right)\right)$

$\mathrm{S1}≔4\mathrm{GegenbauerC}\left(1\,1\,x\right)\mathrm{LaguerreL}\left(2\,1\,y\right)-7\mathrm{GegenbauerC}\left(3\,1\,x\right)\mathrm{LaguerreL}\left(4\,1\,y\right)$

$\mathrm{Coefficients}\left(\mathrm{S1}\right)\;$$\mathrm{Coefficients}\left(\mathrm{S1}\,1\right)\;$$\mathrm{Coefficients}\left(\mathrm{S1}\,\left[1\,2\right]\right)\;$$\mathrm{Coefficients}\left(\mathrm{S1}\,\left[2\,2\right]\right)$

$0$

Error, (in OrthogonalSeries:-Coefficients) index of different dimension than input

$4$

$0$

$\mathrm{S1}≔\mathrm{Create}\left(\left\{a\left(n\,m\right)\,\left[\left(1\,2\right)=4\,\left(3\,4\right)=-7\right]\right\}\,\mathrm{GegenbauerC}\left(n\,1\,x\right)\,\mathrm{LaguerreL}\left(m\,1\,y\right)\right)$

$\mathrm{S1}≔4\mathrm{GegenbauerC}\left(1\,1\,x\right)\mathrm{LaguerreL}\left(2\,1\,y\right)-7\mathrm{GegenbauerC}\left(3\,1\,x\right)\mathrm{LaguerreL}\left(4\,1\,y\right)+\left(\sum _{m=0}^{\mathrm{\infty }}\left(\sum _{n=0}^{\mathrm{\infty }}a\left(n\,m\right)\mathrm{GegenbauerC}\left(n\,1\,x\right)\right)\mathrm{LaguerreL}\left(m\,1\,y\right)\right)$

$\mathrm{Coefficients}\left(\mathrm{S1}\right)\;$$\mathrm{Coefficients}\left(\mathrm{S1}\,\left[1\,2\right]\right)\;$$\mathrm{Coefficients}\left(\mathrm{S1}\,\left[2\,2\right]\right)$

$a\left(n\,m\right)$

$a\left(1\,2\right)+4$

$a\left(2\,2\right)$