18 Orthogonal PolynomialsClassical Orthogonal Polynomials18.3 Definitions18.5 Explicit Representations

§18.4 Graphics

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Permalink:

http://dlmf.nist.gov/18.4

See also:

Annotations for Ch.18

Contents

1. §18.4(i) Graphs
2. §18.4(ii) Surfaces

§18.4(i) Graphs

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Notes:

These graphs were produced at NIST.

Permalink:

http://dlmf.nist.gov/18.4.i

See also:

Annotations for §18.4 and Ch.18

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Symbols:

$P_n^{(\alpha ,\beta )}\left(x\right)$: Jacobi polynomial, $n$: nonnegative integer and $x$: real variable

Keywords:

Jacobi polynomials, graphs

Referenced by:

§18.2(vi)

Permalink:

http://dlmf.nist.gov/18.4.F1

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$P_n^{(\alpha ,\beta )}\left(x\right)$: Jacobi polynomial, $n$: nonnegative integer and $x$: real variable

Keywords:

Jacobi polynomials, graphs

Permalink:

http://dlmf.nist.gov/18.4.F2

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$T_n\left(x\right)$: Chebyshev polynomial of the first kind, $n$: nonnegative integer and $x$: real variable

Keywords:

Chebyshev polynomials, graphs

Referenced by:

§3.11(ii)

Permalink:

http://dlmf.nist.gov/18.4.F3

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$P_n\left(x\right)$: Legendre polynomial, $n$: nonnegative integer and $x$: real variable

Keywords:

Legendre polynomials, graphs

Permalink:

http://dlmf.nist.gov/18.4.F4

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$L_n\left(x\right)=L_n^{(0)}\left(x\right)$: Laguerre polynomial, $n$: nonnegative integer and $x$: real variable

Keywords:

Laguerre polynomials, graphics

Permalink:

http://dlmf.nist.gov/18.4.F5

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$L_n^{(\alpha )}\left(x\right)$: Laguerre (or generalized Laguerre) polynomial and $x$: real variable

Keywords:

Laguerre polynomials, graphics

Permalink:

http://dlmf.nist.gov/18.4.F6

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

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Symbols:

$H_n\left(x\right)$: Hermite polynomial, $n$: nonnegative integer and $x$: real variable

Keywords:

Hermite polynomials, graphs, monic

Referenced by:

§18.2(vi)

Permalink:

http://dlmf.nist.gov/18.4.F7

Encodings:

pdf, png

See also:

Annotations for §18.4(i), §18.4 and Ch.18

§18.4(ii) Surfaces

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Notes:

These surfaces were produced at NIST.

Permalink:

http://dlmf.nist.gov/18.4.ii

See also:

Annotations for §18.4 and Ch.18

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Symbols:

$L_n^{(\alpha )}\left(x\right)$: Laguerre (or generalized Laguerre) polynomial and $x$: real variable

Permalink:

http://dlmf.nist.gov/18.4.F8

Encodings:

Vizualization, pdf, png

See also:

Annotations for §18.4(ii), §18.4 and Ch.18

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Symbols:

$L_n^{(\alpha )}\left(x\right)$: Laguerre (or generalized Laguerre) polynomial and $x$: real variable

Permalink:

http://dlmf.nist.gov/18.4.F9

Encodings:

Vizualization, pdf, png

See also:

Annotations for §18.4(ii), §18.4 and Ch.18

18.3 Definitions18.5 Explicit Representations

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