15 Hypergeometric FunctionProperties15.2 Definitions and Analytical Properties15.4 Special Cases

§15.3 Graphics

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Permalink:

http://dlmf.nist.gov/15.3

See also:

Annotations for Ch.15

Contents

1. §15.3(i) Graphs
2. §15.3(ii) Surfaces

§15.3(i) Graphs

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Keywords:

graphics, hypergeometric function

Notes:

These graphics were produced at NIST.

Permalink:

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

See also:

Annotations for §15.3 and Ch.15

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function and $x$: real variable

Permalink:

http://dlmf.nist.gov/15.3.F1

Encodings:

pdf, png

See also:

Annotations for §15.3(i), §15.3 and Ch.15

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function and $x$: real variable

Permalink:

http://dlmf.nist.gov/15.3.F2

Encodings:

pdf, png

See also:

Annotations for §15.3(i), §15.3 and Ch.15

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function and $x$: real variable

Permalink:

http://dlmf.nist.gov/15.3.F3

Encodings:

pdf, png

See also:

Annotations for §15.3(i), §15.3 and Ch.15

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function and $x$: real variable

Permalink:

http://dlmf.nist.gov/15.3.F4

Encodings:

pdf, png

See also:

Annotations for §15.3(i), §15.3 and Ch.15

§15.3(ii) Surfaces

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Keywords:

graphics, hypergeometric function

Notes:

These graphics were produced at NIST.

Permalink:

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

See also:

Annotations for §15.3 and Ch.15

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.

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function, $\mathrm{i}$: imaginary unit, $x$: real variable and $y$: real variable

Referenced by:

§15.3(ii)

Permalink:

http://dlmf.nist.gov/15.3.F5

Encodings:

Vizualization, pdf, png

See also:

Annotations for §15.3(ii), §15.3 and Ch.15

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Symbols:

$F(a,b;c;z)$ or $F(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}F_1^{}(a,b;c;z)$ Gauss’ hypergeometric function, $\mathrm{i}$: imaginary unit and $c$: real or complex parameter

Referenced by:

§15.2(ii), §15.3(ii)

Permalink:

http://dlmf.nist.gov/15.3.F6

Encodings:

Vizualization, pdf, png

See also:

Annotations for §15.3(ii), §15.3 and Ch.15

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Symbols:

$\mathrm{i}$: imaginary unit and $𝐅(a,b;c;z)$ or $𝐅(\genfrac{}{}{0pt}{}{a,b}{c};z)$: $={}_2{}^{}𝐅_1^{}(a,b;c;z)$ Olver’s hypergeometric function

Referenced by:

§15.2(ii)

Permalink:

http://dlmf.nist.gov/15.3.F7

Encodings:

Vizualization, pdf, png

See also:

Annotations for §15.3(ii), §15.3 and Ch.15

15.2 Definitions and Analytical Properties15.4 Special Cases

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