The Add command is used to numerically add a formula, that is passed as a procedure that depends on a single non-negative integer parameter, say $n$, a summation index, or two of them, say $n$ and $m$. The summation over these parameters starts at 0 and is performed until the result converges (up to Digits). If the formula does not converge, the sum is interrupted when the number of terms added reaches $10000\mathrm{Digits}$, in which case a WARNING message explaining the situation is displayed on the screen.

When a second argument $N$ is passed, if it is a non-negative integer, the summation, that starts at $n=0$, or $n=0$ and $m=0$ in the case of two parameters, is performed until the result converges (up to Digits) or $n=N$. This second argument can also be passed as a range, say $n_0..n_f$, in which case the summation will start at $n_0$ until the result converges or $n_f$ terms were added.

The case of two parameters $n$ and $m$ is handled by rewriting the double sum from 0 to $\mathrm{\infty }$ as a single sum in only one parameter $k$ from 0 to $\mathrm{\infty }$ according to

Add uses option hfloat, which means that, depending on the mathematical contents of the formula_procedure passed, the numerical evaluation will be performed using hardware floating-point values. Depending on the operations performed, this can significantly speed up the execution of the procedure.

Add is mainly useful to numerically evaluate mathematical expressions or functions that can be represented as an infinite sum. In these cases, with Add you can do:

a fast implementation of a numerical evaluation procedure for the expression (see the Examples section);

fast experimentation with different formulas, for instance comparing their performance for numerically evaluating the expression.

Initialization: Load the package and set the display of special functions in output to typeset mathematical notation (textbook notation):

$\mathrm{with}\left(\mathrm{MathematicalFunctions}:-\mathrm{Evalf}\right)\;\mathrm{Typesetting}:-\mathrm{EnableTypesetRule}\left(\mathrm{Typesetting}:-\mathrm{SpecialFunctionRules}\right)\:$

$\left\{\mathrm{Add}\,\mathrm{Evalb}\,\mathrm{Zoom}\,\mathrm{QuadrantNumbers}\,\mathrm{Singularities}\,\mathrm{GenerateRecurrence}\,\mathrm{PairwiseSummation}\right\}$

$\mathrm{FunctionAdvisor}\left(\mathrm{sum}\, \mathrm{SphericalY}\left(\mathrm{lambda}\, \mathrm{mu}\, \mathrm{theta}\, \mathrm{phi}\right)\right)$

* Partial match of "sum" against topic "sum_form".

$\left[Y_{\mathrm{\lambda }}^{\mathrm{\mu }}\left(\mathrm{\theta }\,\mathrm{\phi }\right)=\frac{{\left(\mathrm{-1}\right)}^{\mathrm{\mu }}\sqrt{\frac{2\mathrm{\lambda }+1}{\mathrm{\pi }}}\sqrt{\left(\mathrm{\lambda }-\mathrm{\mu }\right)!}{\ⅇ}^{\mathrm{I}\mathrm{\phi }\mathrm{\mu }}{\left(\cos \left(\mathrm{\theta }\right)+1\right)}^{\frac{\mathrm{\mu }}{2}}\left(\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{{\left(-\mathrm{\lambda }\right)}_{\mathrm{\_k1}}{\left(\mathrm{\lambda }+1\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\mathrm{\theta }\right)}{2}\right)}^{\mathrm{\_k1}}}{\mathrm{\_k1}!{\left(1-\mathrm{\mu }\right)}_{\mathrm{\_k1}}}\right)}{2\sqrt{\left(\mathrm{\lambda }+\mathrm{\mu }\right)!}{\left(\cos \left(\mathrm{\theta }\right)-1\right)}^{\frac{\mathrm{\mu }}{2}}\mathrm{\Gamma }\left(1-\mathrm{\mu }\right)}\,\neg \left(\mathrm{\lambda }+\mathrm{\mu }\right)::{\mathbb{Z}}^{-}\wedge \neg \left(\mathrm{\lambda }-\mathrm{\mu }\right)::{\mathbb{Z}}^{-}\wedge \neg \left(1-\mathrm{\mu }\right)::{\mathbb{Z}}^{\left(0\,-\right)}\right]$

$\mathrm{combine}\left(\mathrm{op}\left(1\,\right)\right)$

$Y_{\mathrm{\lambda }}^{\mathrm{\mu }}\left(\mathrm{\theta }\,\mathrm{\phi }\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{\sqrt{\left(\mathrm{\lambda }-\mathrm{\mu }\right)!}{\left(\cos \left(\mathrm{\theta }\right)+1\right)}^{\frac{\mathrm{\mu }}{2}}{\left(\cos \left(\mathrm{\theta }\right)-1\right)}^{-\frac{\mathrm{\mu }}{2}}\sqrt{\frac{2\mathrm{\lambda }+1}{\mathrm{\pi }}}{\ⅇ}^{\mathrm{I}\mathrm{\phi }\mathrm{\mu }}{\left(\mathrm{-1}\right)}^{\mathrm{\mu }}{\left(-\mathrm{\lambda }\right)}_{\mathrm{\_k1}}{\left(\mathrm{\lambda }+1\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\mathrm{\theta }\right)}{2}\right)}^{\mathrm{\_k1}}}{2\sqrt{\left(\mathrm{\lambda }+\mathrm{\mu }\right)!}\mathrm{\Gamma }\left(1-\mathrm{\mu }\right)\mathrm{\_k1}!{\left(1-\mathrm{\mu }\right)}_{\mathrm{\_k1}}}$

$\mathrm{summand}≔\mathrm{op}\left(1\,\mathrm{rhs}\left(\right)\right)$

$\mathrm{summand}≔\frac{\sqrt{\left(\mathrm{\lambda }-\mathrm{\mu }\right)!}{\left(\cos \left(\mathrm{\theta }\right)+1\right)}^{\frac{\mathrm{\mu }}{2}}{\left(\cos \left(\mathrm{\theta }\right)-1\right)}^{-\frac{\mathrm{\mu }}{2}}\sqrt{\frac{2\mathrm{\lambda }+1}{\mathrm{\pi }}}{\ⅇ}^{\mathrm{I}\mathrm{\phi }\mathrm{\mu }}{\left(\mathrm{-1}\right)}^{\mathrm{\mu }}{\left(-\mathrm{\lambda }\right)}_{\mathrm{\_k1}}{\left(\mathrm{\lambda }+1\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\mathrm{\theta }\right)}{2}\right)}^{\mathrm{\_k1}}}{2\sqrt{\left(\mathrm{\lambda }+\mathrm{\mu }\right)!}\mathrm{\Gamma }\left(1-\mathrm{\mu }\right)\mathrm{\_k1}!{\left(1-\mathrm{\mu }\right)}_{\mathrm{\_k1}}}$

$\mathrm{subs}\left(\left[\mathrm{lambda} \= \frac{1}{2}\, \mathrm{mu} \= \frac{3}{2}\+I\, \mathrm{phi} \=\frac{\mathrm{Pi}}{7}\, \mathrm{theta} \= \frac{1}{3}\+\frac{I}{5}\right]\, \mathrm{summand}\right)$

$\frac{\sqrt{\left(\mathrm{-1}-\mathrm{I}\right)!}{\left(\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)+1\right)}^{\frac{3}{4}+\frac{\mathrm{I}}{2}}{\left(\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)-1\right)}^{-\frac{3}{4}-\frac{\mathrm{I}}{2}}\sqrt{2}\sqrt{\frac{1}{\mathrm{\pi }}}{\ⅇ}^{\left(-\frac{1}{7}+\frac{3\mathrm{I}}{14}\right)\mathrm{\pi }}{\left(\mathrm{-1}\right)}^{\frac{3}{2}+\mathrm{I}}{\left(-\frac{1}{2}\right)}_{\mathrm{\_k1}}{\left(\frac{3}{2}\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)}{2}\right)}^{\mathrm{\_k1}}}{2\sqrt{\left(2+\mathrm{I}\right)!}\mathrm{\Gamma }\left(-\frac{1}{2}-\mathrm{I}\right)\mathrm{\_k1}!{\left(-\frac{1}{2}-\mathrm{I}\right)}_{\mathrm{\_k1}}}$

$\mathrm{formula\_procedure}≔\mathrm{unapply}\left(\,\mathrm{\_k1}\right)$

$\mathrm{formula\_procedure}≔\mathrm{\_k1}\mapsto \frac{\sqrt{\left(\mathrm{-1}-\mathrm{I}\right)!}{\left(\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)+1\right)}^{\frac{3}{4}+\frac{\mathrm{I}}{2}}{\left(\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)-1\right)}^{-\frac{3}{4}-\frac{\mathrm{I}}{2}}\sqrt{2}\sqrt{\frac{1}{\mathrm{\pi }}}{\ⅇ}^{\left(-\frac{1}{7}+\frac{3\mathrm{I}}{14}\right)\mathrm{\pi }}{\left(\mathrm{-1}\right)}^{\frac{3}{2}+\mathrm{I}}{\left(-\frac{1}{2}\right)}_{\mathrm{\_k1}}{\left(\frac{3}{2}\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\frac{1}{3}+\frac{\mathrm{I}}{5}\right)}{2}\right)}^{\mathrm{\_k1}}}{2\sqrt{\left(2+\mathrm{I}\right)!}\mathrm{\Gamma }\left(-\frac{1}{2}-\mathrm{I}\right)\mathrm{\_k1}!{\left(-\frac{1}{2}-\mathrm{I}\right)}_{\mathrm{\_k1}}}$

$\mathrm{Add}\left(\mathrm{formula\_procedure}\right)$

$0.05489806051-0.01484631132\mathrm{I}$

$\mathrm{general\_formula}≔\mathrm{unapply}\left(\mathrm{summand}\,\mathrm{\_k1}\right)$

$\mathrm{general\_formula}≔\mathrm{\_k1}\mapsto \frac{\sqrt{\left(\mathrm{\lambda }-\mathrm{\mu }\right)!}{\left(\cos \left(\mathrm{\theta }\right)+1\right)}^{\frac{\mathrm{\mu }}{2}}{\left(\cos \left(\mathrm{\theta }\right)-1\right)}^{-\frac{\mathrm{\mu }}{2}}\sqrt{\frac{2\mathrm{\lambda }+1}{\mathrm{\pi }}}{\ⅇ}^{\mathrm{I}\mathrm{\phi }\mathrm{\mu }}{\left(\mathrm{-1}\right)}^{\mathrm{\mu }}{\left(-\mathrm{\lambda }\right)}_{\mathrm{\_k1}}{\left(\mathrm{\lambda }+1\right)}_{\mathrm{\_k1}}{\left(\frac{1}{2}-\frac{\cos \left(\mathrm{\theta }\right)}{2}\right)}^{\mathrm{\_k1}}}{2\sqrt{\left(\mathrm{\lambda }+\mathrm{\mu }\right)!}\mathrm{\Gamma }\left(1-\mathrm{\mu }\right)\mathrm{\_k1}!{\left(1-\mathrm{\mu }\right)}_{\mathrm{\_k1}}}$

$\mathrm{`evalf/Y`} ≔ \left(\mathrm{lambda}\, \mathrm{mu}\, \mathrm{theta}\, \mathrm{phi}\right) \to \mathrm{Add}\left(\mathrm{subs}\left(\'\left[:-\mathrm{lambda} \= \mathrm{lambda}\, :-\mathrm{mu} \= \mathrm{mu}\, :-\mathrm{theta} \= \mathrm{theta}\, :-\mathrm{phi} \= \mathrm{phi}\right]\'\, \mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$\mathrm{evalf/Y}≔\left(\mathrm{\lambda }\,\mathrm{\mu }\,\mathrm{\theta }\,\mathrm{\phi }\right)\mapsto \mathrm{Add}\left(\mathrm{subs}\left('\left[:-\mathrm{\lambda }=\mathrm{\lambda }\,:-\mathrm{\mu }=\mathrm{\mu }\,:-\mathrm{\theta }=\mathrm{\theta }\,:-\mathrm{\phi }=\mathrm{\phi }\right]'\,\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$Y\left(\frac{1}{2}\, \frac{3}{2}\+I\, \frac{1}{3}\+\frac{I}{5}\, \frac{\mathrm{Pi}}{7}\right)$

$Y\left(\frac{1}{2}\,\frac{3}{2}+\mathrm{I}\,\frac{1}{3}+\frac{\mathrm{I}}{5}\,\frac{\mathrm{\pi }}{7}\right)$

$\mathrm{evalf}\left(\right)$

$0.05489806051-0.01484631132\mathrm{I}$

$\mathrm{plot}\left(\mathrm{Re}\left(Y\left(\frac{1}{2}\, \frac{3}{2}\+I\, \frac{1}{3}\+\frac{I}{5}\, \mathrm{theta}\right)\right)\, \mathrm{theta} \= 0 .. \mathrm{Pi}\right)$

$\mathrm{plot}\left(\mathrm{Re}\left(\mathrm{SphericalY}\left(\frac{1}{2}\, \frac{3}{2}\+I\, \frac{1}{3}\+\frac{I}{5}\, \mathrm{theta}\right)\right)\, \mathrm{theta} \= 0 .. \mathrm{Pi}\right)$

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

* Partial match of "sum" against topic "sum_form".

$\left[{\mathrm{Ei}}_a\left(z\right)=\left(\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{{\left(-z\right)}^{\mathrm{\_k1}}}{\mathrm{\Gamma }\left(\mathrm{\_k1}+1\right)\left(-1+a-\mathrm{\_k1}\right)}\right)+z^{a-1}\mathrm{\Gamma }\left(1-a\right)\,a::\left(\neg {\mathbb{Z}}^{+}\right)\right],\left[{\mathrm{Ei}}_a\left(z\right)=\left(\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\frac{{\left(\mathrm{-1}\right)}^{a+2\mathrm{\_k1}}\left(-\mathrm{\Psi }\left(\mathrm{\_k1}+1\right)+\ln \left(z\right)\right)z^{a-1+\mathrm{\_k1}}}{\mathrm{\Gamma }\left(\mathrm{\_k1}+1\right)\mathrm{\Gamma }\left(a\right){\ⅇ}^z}\right)+\left(\sum _{\mathrm{\_k1}=0}^{-2+a}\frac{{\left(\mathrm{-1}\right)}^{\mathrm{\_k1}}\mathrm{\Gamma }\left(-1+a-\mathrm{\_k1}\right)z^{\mathrm{\_k1}}}{\mathrm{\Gamma }\left(a\right){\ⅇ}^z}\right)\,a::{\mathbb{Z}}^{+}\wedge z\ne 0\right],\left[{\mathrm{Ei}}_a\left(z\right)=\sum _{\mathrm{\_k1}=0}^{-a}\frac{\left(-a\right)!z^{a-1+\mathrm{\_k1}}}{{\ⅇ}^z\mathrm{\_k1}!}\,a::{\mathbb{Z}}^{-}\wedge z\ne 0\right]$

$\mathrm{summand}≔\mathrm{op}\left(1\,\mathrm{rhs}\left(\left(\left[-1\right]\right)\left[1\right]\right)\right)$

$\mathrm{summand}≔\frac{\left(-a\right)!z^{a-1+\mathrm{\_k1}}}{{\ⅇ}^z\mathrm{\_k1}!}$

$\mathrm{general\_formula}≔\mathrm{unapply}\left(\mathrm{summand}\,\mathrm{\_k1}\right)$

$\mathrm{general\_formula}≔\mathrm{\_k1}\mapsto \frac{\left(-a\right)!z^{a-1+\mathrm{\_k1}}}{{\ⅇ}^z\mathrm{\_k1}!}$

$\mathrm{`evalf/EI`}≔\left(a\,z\right)\→\mathrm{Add}\left(\mathrm{subs}\left(\'\left[:-a\=a\,:-z\=z\right]\'\,\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$\mathrm{evalf/EI}≔\left(a\,z\right)\mapsto \mathrm{Add}\left(\mathrm{subs}\left('\left[:-a=a\,:-z=z\right]'\,\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$\mathrm{infolevel}\left[\mathrm{Add}\right] ≔ 5$

${\mathrm{infolevel}}_{\mathrm{Add}}≔5$

$\mathrm{EI}\left(-4\,\frac{21}{50}-\frac{3\mathrm{I}}{10}\right)$

$\mathrm{EI}\left(\mathrm{-4}\,\frac{21}{50}-\frac{3\mathrm{I}}{10}\right)$

$\mathrm{evalf}\left(\right)$

    -> entering Add with: 'formula' = 24/exp(21/50-3/10*I)/k!*(21/50-3/10*I)^(-5+k)
    <- exiting Add with -654.669541617+26.4271294535*I; after adding 17 terms

$\mathrm{-654.6695416}+26.42712945\mathrm{I}$

$\mathrm{Ei}\left(-4\&comma;\frac{21}{50}-\frac{3 I}{10}\right)$

${\mathrm{Ei}}_{\mathrm{-4}}\left(\frac{21}{50}-\frac{3\mathrm{I}}{10}\right)$

$\mathrm{evalf}\left(\right)$

$\mathrm{-654.8063012}+26.39258365\mathrm{I}$

$\mathrm{`evalf/EI`}≔\left(a::\mathrm{negint}\&comma;z\right)\&rarr;\mathrm{Add}\left(\mathrm{subs}\left(\&apos;\left[:-a\&equals;a\&comma;:-z\&equals;z\right]\&apos;\&comma;\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\&comma;-a\right)$

$\mathrm{evalf/EI}≔\left(a::{\mathbb{Z}}^{-}\&comma;z\right)\mapsto \mathrm{Add}\left(\mathrm{subs}\left('\left[:-a=a\&comma;:-z=z\right]'\&comma;\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\&comma;-a\right)$

$\mathrm{forget}\left(\mathrm{evalf}\right)$

$\mathrm{evalf}\left(\right)$

    -> entering Add with: 'formula' = 24/exp(21/50-3/10*I)/k!*(21/50-3/10*I)^(-5+k)

    <- exiting Add with -654.806301169+26.3925836556*I; after adding 5 terms

$\mathrm{-654.8063012}+26.39258366\mathrm{I}$

$\mathrm{evalf}\left(\mathrm{EI}\left(1\&comma;\frac{21}{50}-\frac{3\mathrm{I}}{10}\right)\right)$

Error, invalid input: `evalf/EI` expects its 1st argument, a, to be of type negint, but received 1

$\mathrm{FunctionAdvisor}\left(\mathrm{definition}\&comma; \mathrm{AppellF2}\left(a\&comma; \mathrm{b1}\&comma; \mathrm{b2}\&comma; \mathrm{c1}\&comma; \mathrm{c2}\&comma; \mathrm{z1}\&comma; \mathrm{z2}\right)\right)$

$\left[F_2\left(a\&comma;\mathrm{b1}\&comma;\mathrm{b2}\&comma;\mathrm{c1}\&comma;\mathrm{c2}\&comma;\mathrm{z1}\&comma;\mathrm{z2}\right)=\sum _{\mathrm{\_k1}=0}^{\mathrm{\infty }}\sum _{\mathrm{\_k2}=0}^{\mathrm{\infty }}\frac{{\left(a\right)}_{\mathrm{\_k1}+\mathrm{\_k2}}{\left(\mathrm{b1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{b2}\right)}_{\mathrm{\_k2}}{\mathrm{z1}}^{\mathrm{\_k1}}{\mathrm{z2}}^{\mathrm{\_k2}}}{{\left(\mathrm{c1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{c2}\right)}_{\mathrm{\_k2}}\mathrm{\_k1}!\mathrm{\_k2}!}\&comma;\left|\mathrm{z1}\right|+\left|\mathrm{z2}\right|<1\right]$

$\mathrm{summand}≔\mathrm{op}\left(\left[1\&comma;1\right]\&comma;\mathrm{rhs}\left({}_{}\left[1\right]\right)\right)$

$\mathrm{summand}≔\frac{{\left(a\right)}_{\mathrm{\_k1}+\mathrm{\_k2}}{\left(\mathrm{b1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{b2}\right)}_{\mathrm{\_k2}}{\mathrm{z1}}^{\mathrm{\_k1}}{\mathrm{z2}}^{\mathrm{\_k2}}}{{\left(\mathrm{c1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{c2}\right)}_{\mathrm{\_k2}}\mathrm{\_k1}!\mathrm{\_k2}!}$

$\mathrm{general\_formula}≔\mathrm{unapply}\left(\mathrm{summand}\&comma;\mathrm{\_k1}\&comma;\mathrm{\_k2}\right)$

$\mathrm{general\_formula}≔\left(\mathrm{\_k1}\&comma;\mathrm{\_k2}\right)\mapsto \frac{{\left(a\right)}_{\mathrm{\_k1}+\mathrm{\_k2}}{\left(\mathrm{b1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{b2}\right)}_{\mathrm{\_k2}}{\mathrm{z1}}^{\mathrm{\_k1}}{\mathrm{z2}}^{\mathrm{\_k2}}}{{\left(\mathrm{c1}\right)}_{\mathrm{\_k1}}{\left(\mathrm{c2}\right)}_{\mathrm{\_k2}}\mathrm{\_k1}!\mathrm{\_k2}!}$

$\mathrm{`evalf/AF2`}≔\left(a\&comma;\mathrm{b1}\&comma;\mathrm{b2}\&comma;\mathrm{c1}\&comma;\mathrm{c2}\&comma;\mathrm{z1}\&comma;\mathrm{z2}\right)\&rarr;\mathrm{Add}\left(\mathrm{subs}\left(\&apos;\left[:-a\&equals;a\&comma;:-\mathrm{b1}\&equals;\mathrm{b1}\&comma;:-\mathrm{b2}\&equals;\mathrm{b2}\&comma;:-\mathrm{c1}\&equals;\mathrm{c1}\&comma;:-\mathrm{c2}\&equals;\mathrm{c2}\&comma;:-\mathrm{z1}\&equals;\mathrm{z1}\&comma;:-\mathrm{z2}\&equals;\mathrm{z2}\right]\&apos;\&comma;\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$\mathrm{evalf/AF2}≔\left(a\&comma;\mathrm{b1}\&comma;\mathrm{b2}\&comma;\mathrm{c1}\&comma;\mathrm{c2}\&comma;\mathrm{z1}\&comma;\mathrm{z2}\right)\mapsto \mathrm{Add}\left(\mathrm{subs}\left('\left[:-a=a\&comma;:-\mathrm{b1}=\mathrm{b1}\&comma;:-\mathrm{b2}=\mathrm{b2}\&comma;:-\mathrm{c1}=\mathrm{c1}\&comma;:-\mathrm{c2}=\mathrm{c2}\&comma;:-\mathrm{z1}=\mathrm{z1}\&comma;:-\mathrm{z2}=\mathrm{z2}\right]'\&comma;\mathrm{eval}\left(\mathrm{general\_formula}\right)\right)\right)$

$\mathrm{AF2}\left(\frac{1}{2}\&comma;\frac{2}{7}\&comma;-\frac{1}{4}\&comma;2\&comma;\frac{3}{2}+\mathrm{I}\&comma;\frac{1}{4}\mathrm{I}\&comma;\frac{1}{4}\right)$

$\mathrm{AF2}\left(\frac{1}{2}\&comma;\frac{2}{7}\&comma;-\frac{1}{4}\&comma;2\&comma;\frac{3}{2}+\mathrm{I}\&comma;\frac{\mathrm{I}}{4}\&comma;\frac{1}{4}\right)$

$\mathrm{evalf}\left(\right)$

    -> entering Add with: 'formula' = add(pochhammer(1/2,k+m)*pochhammer(2/7,k)*pochhammer(-1/4,m)*(1/4*I)^k*(1/4)^m/pochhammer(2,k)/pochhammer(3/2+I,m)/k!/m!,m = 0 .. k)+add(pochhammer(1/2,n+k)*pochhammer(2/7,n)*pochhammer(-1/4,k)*(1/4*I)^n*(1/4)^k/pochhammer(2,n)/pochhammer(3/2+I,k)/n!/k!,n = 0 .. k-1)

    <- exiting Add with .983152249087+.272658733829e-1*I; after adding 19 terms

$0.9831522491+0.02726587338\mathrm{I}$

$\mathrm{subs}\left(\mathrm{AF2}=\mathrm{AppellF2}\&comma;\right)$

$F_2\left(\frac{1}{2}\&comma;\frac{2}{7}\&comma;-\frac{1}{4}\&comma;2\&comma;\frac{3}{2}+\mathrm{I}\&comma;\frac{\mathrm{I}}{4}\&comma;\frac{1}{4}\right)$

$\mathrm{evalf}\left(\right)$

$0.9831522491+0.02726587338\mathrm{I}$

The MathematicalFunctions[Evalf][Add] command was introduced in Maple 2017.

For more information on Maple 2017 changes, see Updates in Maple 2017.