The FunctionAdvisor(sum_form, math_function) command returns the sum form of the function if it exists.

$\mathrm{FunctionAdvisor}\left(\mathrm{sum\_form}\,\mathrm{StruveL}\right)$

$\left[\mathrm{StruveL}\left(a\,z\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{-\frac{\mathrm{I}}{2}{\left(\mathrm{-1}\right)}^{\frac{a}{2}+\frac{1}{2}+2\mathrm{\_k1}}{z}^{a+1+2\mathrm{\_k1}}}{{\ⅇ}^{\frac{\mathrm{I}}{2}a\mathrm{\pi }}{2}^{a+2\mathrm{\_k1}}\mathrm{\Gamma }\left(\frac{3}{2}+\mathrm{\_k1}\right)\mathrm{\Gamma }\left(\frac{3}{2}+a+\mathrm{\_k1}\right)}\,\left(a+\frac{3}{2}\right)::\left(\neg {\mathbb{Z}}^{\left(0\,+\right)}\right)\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{sum\_form}\,\mathrm{JacobiTheta1}\left(a\,z\right)\right)$

$\left[\mathrm{JacobiTheta1}\left(a\&comma;z\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}2z^{{\left(\mathrm{\_k1}+\frac{1}{2}\right)}^2}\sin \left(a\left(2\mathrm{\_k1}+1\right)\right){\left(\mathrm{-1}\right)}^{\mathrm{\_k1}}\&comma;\left|z\right|<1\right]$

$\mathrm{FunctionAdvisor}\left(\mathrm{sum\_form}\&comma;\cos \right)$

$\left[\cos \left(z\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{{\left(\mathrm{-1}\right)}^{\mathrm{\_k1}}{z}^{2\mathrm{\_k1}}}{\left(2\mathrm{\_k1}\right)!}\&comma;\mathrm{with\; no\; restrictions\; on}\left(z\right)\right]$

$\mathrm{depends}\left(\mathrm{FunctionAdvisor}\left(\mathrm{sum\_form}\&comma;\cos \right)\&comma;z\right)$

$\mathrm{false}$

$f≔\mathrm{FunctionAdvisor}\left(\mathrm{sum\_form}\&comma;\mathrm{Stirling1}\left(n\&comma;z\right)\right)$

$f≔\left[\mathrm{Stirling1}\left(n\&comma;z\right)=\sum _{\mathrm{\_k1}=0}^{n-z}\sum _{\mathrm{\_k2}=0}^{\mathrm{\_k1}}\frac{{\left(\mathrm{-1}\right)}^{2\mathrm{\_k1}-\mathrm{\_k2}}\left(\genfrac{}{}{0ex}{}{n-1+\mathrm{\_k1}}{n-z+\mathrm{\_k1}}\right)\left(\genfrac{}{}{0ex}{}{2n-z}{n-z-\mathrm{\_k1}}\right)\left(\genfrac{}{}{0ex}{}{\mathrm{\_k1}}{\mathrm{\_k2}}\right){\mathrm{\_k2}}^{n-z+\mathrm{\_k1}}}{\mathrm{\_k1}!}\&comma;n::{\mathbb{Z}}^{\left(0\&comma;+\right)}\wedge z::{\mathbb{Z}}^{\left(0\&comma;+\right)}\right]$

$\mathrm{depends}\left(f\&comma;n\right),\mathrm{depends}\left(f\&comma;z\right)$

$\mathrm{true},\mathrm{true}$