The FunctionAdvisor(series, math_function) command returns the series expansion of the function when the system can compute it. Otherwise, the command returns NULL.

The order of the series expansion in the output is set to four. On the left-hand side there is the corresponding function call to compute the series in Maple to facilitate copy and paste. If you change the order in the calling sequence, it returns the number of terms requested.

$\mathrm{FunctionAdvisor}\left(\mathrm{series}\,\mathrm{JacobiTheta3}\right)$

$\mathrm{series}\left(\mathrm{JacobiTheta3}\left(z\,q\right)\,z\,4\right)=2\left(\sum _{\mathrm{\_k1}=1}^{\mathrm{\infty }}{q}^{{\mathrm{\_k1}}^2}\right)+1-4\left(\sum _{\mathrm{\_k1}=1}^{\mathrm{\infty }}{q}^{{\mathrm{\_k1}}^2}{\mathrm{\_k1}}^2\right)z^2+O\left(z^4\right),\mathrm{series}\left(\mathrm{JacobiTheta3}\left(z\,q\right)\,q\,4\right)=1+2\cos \left(2z\right)q+O\left(q^4\right)$

$\mathrm{FunctionAdvisor}\left(\mathrm{series}\,\sin \right)$

$\mathrm{series}\left(\sin \left(z\right)\,z\,4\right)=z-\frac{1}{6}{z}^3+O\left(z^5\right)$

$\mathrm{depends}\left(\,z\right)$

$\mathrm{false}$

$\mathrm{FunctionAdvisor}\left(\mathrm{series}\,\sin \left(z\right)\right)$

$\mathrm{series}\left(\sin \left(z\right)\,z\,4\right)=z-\frac{1}{6}{z}^3+O\left(z^5\right)$

$\mathrm{depends}\left(\,z\right)$

$\mathrm{true}$

$\mathrm{FunctionAdvisor}\left(\mathrm{series}\,\mathrm{{\rm B}}\right)$

$\mathrm{series}\left(\mathrm{{\rm B}}\left(x\,y\right)\,x\,4\right)=x^{\mathrm{-1}}+-\mathrm{\Psi }\left(y\right)-\mathrm{\gamma }+\left(\frac{{\mathrm{\pi }}^2}{12}+\frac{{\mathrm{\gamma }}^2}{2}-\frac{\mathrm{\Psi }\left(1\,y\right)}{2}+\frac{{\mathrm{\Psi }\left(y\right)}^2}{2}+\mathrm{\Psi }\left(y\right)\mathrm{\gamma }\right)x+\left(-\frac{\mathrm{\zeta }\left(3\right)}{3}-\frac{{\mathrm{\pi }}^2\mathrm{\gamma }}{12}-\frac{{\mathrm{\gamma }}^3}{6}-\frac{\mathrm{\Psi }\left(2\,y\right)}{6}+\frac{\mathrm{\Psi }\left(1\,y\right)\mathrm{\Psi }\left(y\right)}{2}-\frac{{\mathrm{\Psi }\left(y\right)}^3}{6}+\frac{\mathrm{\gamma }\mathrm{\Psi }\left(1\,y\right)}{2}-\frac{\mathrm{\gamma }{\mathrm{\Psi }\left(y\right)}^2}{2}-\frac{\mathrm{\Psi }\left(y\right){\mathrm{\gamma }}^2}{2}-\frac{\mathrm{\Psi }\left(y\right){\mathrm{\pi }}^2}{12}\right)x^2+O\left(x^3\right)$