15 Hypergeometric Function Properties 15.2 Definitions and Analytical Properties 15.4 Special Cases

§15.3 Graphics

Permalink:: http://dlmf.nist.gov/15.3

§15.3(i) Graphs
§15.3(ii) Surfaces

§15.3(i) Graphs

Notes:: These graphics were produced at NIST.
Keywords:: hypergeometric function
Permalink:: http://dlmf.nist.gov/15.3.i

Figure 15.3.1: $\mathop{F\/}\nolimits\!\left(\tfrac{4}{3},\tfrac{9}{16};\tfrac{14}{5};x\right)% ,-100\leq x\leq 1$ .

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function and : real variable
Permalink:: http://dlmf.nist.gov/15.3.F1
Encodings:: pdf, png

Figure 15.3.2: $\mathop{F\/}\nolimits\!\left(5,-10;1;x\right),-0.023\leq x\leq 1$ .

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function and : real variable
Permalink:: http://dlmf.nist.gov/15.3.F2
Encodings:: pdf, png

Figure 15.3.3: $\mathop{F\/}\nolimits\!\left(1,-10;10;x\right),-3\leq x\leq 1$ .

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function and : real variable
Permalink:: http://dlmf.nist.gov/15.3.F3
Encodings:: pdf, png

Figure 15.3.4: $\mathop{F\/}\nolimits\!\left(5,10;1;x\right),-1\leq x\leq 0.022$ .

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function and : real variable
Permalink:: http://dlmf.nist.gov/15.3.F4
Encodings:: pdf, png

§15.3(ii) Surfaces

Notes:: These graphics were produced at NIST.
Keywords:: hypergeometric function
Permalink:: http://dlmf.nist.gov/15.3.ii

In Figures 15.3.5 and 15.3.6, height corresponds to the absolute value of the function and color to the phase. See also About Color Map.

Visualization Help

Figure 15.3.5: $\mathop{F\/}\nolimits\!\left(\tfrac{4}{3},\tfrac{9}{16};\tfrac{14}{5};x+iy% \right),0\leq x\leq 2,-0.5\leq y\leq 0.5$ . (There is a cut along the real axis from 1 to $\infty$ .)

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function, : real variable and : real variable
Referenced by:: §15.3(ii)
Permalink:: http://dlmf.nist.gov/15.3.F5
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 15.3.6: $\mathop{F\/}\nolimits\!\left(-3,\frac{3}{5};u+iv;\frac{1}{2}\right),-6\leq u% \leq 2,-2\leq v\leq 2$ . (With

the only poles occur at

; compare §15.2(ii).)

Symbols:: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$ : hypergeometric function and : real or complex parameter
Referenced by:: §15.2(ii), §15.3(ii)
Permalink:: http://dlmf.nist.gov/15.3.F6
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 15.3.7: $|\mathop{\mathbf{F}\/}\nolimits\!\left(-3,\frac{3}{5};u+iv;\frac{1}{2}\right)|% ,-6\leq u\leq 2,-2\leq v\leq 2$ .

Symbols:: $\mathop{\mathbf{F}\/}\nolimits\!\left(a,b;c;z\right)$ : Olver’s hypergeometric function
Referenced by:: §15.2(ii)
Permalink:: http://dlmf.nist.gov/15.3.F7
Encodings:: VRML, X3D, pdf, png

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 15.2 Definitions and Analytical Properties 15.4 Special Cases

§15.3 Graphics

Contents

§15.3(i) Graphs

§15.3(ii) Surfaces