DLMF: Figure 15.3.6 ‣ §15.3 Graphics ‣ Properties ‣ Chapter 15 Hypergeometric Function

15 Hypergeometric Function Properties 15.3 Graphics 15.3 Graphics 15.4 Special Cases

Figure 15.3.6 (See in context.)

Figure 15.3.6:

F\left(-3,\frac{3}{5};u+\mathrm{i}v;\frac{1}{2}\right),-6\leq u\leq 2,-2\leq v\leq 2

. (With

c=u+\mathrm{i}v

the only poles occur at

c=0,-1,-2

; compare §15.2(ii).)

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Annotations:

Symbols:: $F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ or $F\left({\NVar{a},\NVar{b}\atop\NVar{c}};\NVar{z}\right)$ : $={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$ Gauss’ hypergeometric function, $\mathrm{i}$ : imaginary unit and $c$ : real or complex parameter
Permalink:: http://dlmf.nist.gov/15.3.F6.viz

15.3 Graphics 15.4 Special Cases

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