The AddFunction(g, f) command, a library extension mechanism, adds a definition related to the function g to MultiSeries, where f is a user-defined procedure which handles multiseries containing the function g.

For example, let f be a user-defined function for g.  To add this information to the multiseries function, use AddFunction(g, eval(f,1)).

For example, after issuing AddFunction(g, f), the function call $\mathrm{multiseries}\left(f\left(x\right)\,x\,3\right)$ will invoke $g\left(s\,\mathrm{scale}\,\mathrm{varlist}\,3\right)$ to compute the multiseries. The arguments are the multiseries expansion of the argument of $f$, the scale in which the expansion is performed, the variable with respect to which the expansion is computed, and the order (see multiseries). Note that the function g must return a SERIES data structure or 0, not just a polynomial (see type[SERIES]).

The RemoveFunction(g) command removes a definition related to the function g from the multiseries function.

For example, to remove the information from the multiseries function, use RemoveFunction(g).

The GetFunction(g) command returns a procedure related to the function g, provided that such a procedure exists. Otherwise, it returns NULL.

The FunctionSupported(g) command returns true if a definition of the function g is known to the multiseries function. It returns false otherwise.

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

$\mathrm{series}\left(\mathrm{mysin}\left(x\right)\,x\right)$

$\mathrm{mysin}\left(0\right)+\mathrm{D}\left(\mathrm{mysin}\right)\left(0\right)x+\frac{1}{2}{\mathrm{D}}^{\left(2\right)}\left(\mathrm{mysin}\right)\left(0\right)x^2+\frac{1}{6}{\mathrm{D}}^{\left(3\right)}\left(\mathrm{mysin}\right)\left(0\right)x^3+\frac{1}{24}{\mathrm{D}}^{\left(4\right)}\left(\mathrm{mysin}\right)\left(0\right)x^4+\frac{1}{120}{\mathrm{D}}^{\left(5\right)}\left(\mathrm{mysin}\right)\left(0\right)x^5+O\left(x^6\right)$

$\mathrm{AddFunction}\left(\mathrm{mysin}\,\mathrm{eval}\left(\mathrm{GetFunction}\left(\sin \right)\right)\right)$

$\mathrm{series}\left(\mathrm{mysin}\left(x\right)\,x\right)$

$\mathrm{mysin}\left(0\right)+\mathrm{D}\left(\mathrm{mysin}\right)\left(0\right)x+\frac{1}{2}{\mathrm{D}}^{\left(2\right)}\left(\mathrm{mysin}\right)\left(0\right)x^2+\frac{1}{6}{\mathrm{D}}^{\left(3\right)}\left(\mathrm{mysin}\right)\left(0\right)x^3+\frac{1}{24}{\mathrm{D}}^{\left(4\right)}\left(\mathrm{mysin}\right)\left(0\right)x^4+\frac{1}{120}{\mathrm{D}}^{\left(5\right)}\left(\mathrm{mysin}\right)\left(0\right)x^5+O\left(x^6\right)$

$\mathrm{FunctionSupported}\left(\sin \right)$

$\mathrm{true}$

$\mathrm{RemoveFunction}\left(\sin \right)$

$\mathrm{FunctionSupported}\left(\sin \right)$

$\mathrm{false}$

$\mathrm{AddFunction}\left(\sin \,\mathrm{eval}\left(\mathrm{GetFunction}\left(\mathrm{mysin}\right)\right)\right)$

$\mathrm{RemoveFunction}\left(\mathrm{mysin}\right)$

$\mathrm{FunctionSupported}\left(\sin \right)$

$\mathrm{true}$

$\mathrm{FunctionSupported}\left(\mathrm{mysin}\right)$

$\mathrm{false}$

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

$x-\frac{1}{6}{x}^3+\frac{1}{120}{x}^5+O\left(x^7\right)$

$\mathrm{series}\left(\mathrm{mysin}\left(x\right)\,x\right)$

$\mathrm{mysin}\left(0\right)+\mathrm{D}\left(\mathrm{mysin}\right)\left(0\right)x+\frac{1}{2}{\mathrm{D}}^{\left(2\right)}\left(\mathrm{mysin}\right)\left(0\right)x^2+\frac{1}{6}{\mathrm{D}}^{\left(3\right)}\left(\mathrm{mysin}\right)\left(0\right)x^3+\frac{1}{24}{\mathrm{D}}^{\left(4\right)}\left(\mathrm{mysin}\right)\left(0\right)x^4+\frac{1}{120}{\mathrm{D}}^{\left(5\right)}\left(\mathrm{mysin}\right)\left(0\right)x^5+O\left(x^6\right)$