§18.4 Graphics

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

§18.4(i) Graphs
§18.4(ii) Surfaces

§18.4(i) Graphs

Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/18.4.i

Figure 18.4.1: Jacobi polynomials $\mathop{P^{{(1.5,-0.5)}}_{{n}}\/}\nolimits\!\left(x\right)$ , $n=1,2,3,4,5$ .

Symbols:: $\mathop{P^{{(\alpha,\beta)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Jacobi polynomial, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Jacobi polynomials
Referenced by:: §18.2(vi)
Permalink:: http://dlmf.nist.gov/18.4.F1
Encodings:: pdf, png

Figure 18.4.2: Jacobi polynomials $\mathop{P^{{(1.25,0.75)}}_{{n}}\/}\nolimits\!\left(x\right)$ , $n=7,8$ . This illustrates inequalities for extrema of a Jacobi polynomial; see (18.14.16). See also Askey (1990).

Symbols:: $\mathop{P^{{(\alpha,\beta)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Jacobi polynomial, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Jacobi polynomials
Permalink:: http://dlmf.nist.gov/18.4.F2
Encodings:: pdf, png

Figure 18.4.3: Chebyshev polynomials $\mathop{T_{{n}}\/}\nolimits\!\left(x\right)$ , $n=1,2,3,4,5$ .

Symbols:: $\mathop{T_{{n}}\/}\nolimits\!\left(x\right)$ : Chebyshev polynomial of the first kind, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Chebyshev polynomials
Referenced by:: ¶ ‣ §3.11(ii)
Permalink:: http://dlmf.nist.gov/18.4.F3
Encodings:: pdf, png

Figure 18.4.4: Legendre polynomials $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ , $n=1,2,3,4,5$ .

Symbols:: $\mathop{P_{{n}}\/}\nolimits\!\left(x\right)$ : Legendre polynomial, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Legendre polynomials
Permalink:: http://dlmf.nist.gov/18.4.F4
Encodings:: pdf, png

Figure 18.4.5: Laguerre polynomials $\mathop{L_{{n}}\/}\nolimits\!\left(x\right)$ , $n=1,2,3,4,5$ .

Symbols:: $\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Laguerre (or generalized Laguerre) polynomial, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Laguerre polynomials
Permalink:: http://dlmf.nist.gov/18.4.F5
Encodings:: pdf, png

Figure 18.4.6: Laguerre polynomials $\mathop{L^{{(\alpha)}}_{{3}}\/}\nolimits\!\left(x\right)$ , $\alpha=0,1,2,3,4$ .

Symbols:: $\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Laguerre (or generalized Laguerre) polynomial and $x$ : real variable
Keywords:: Laguerre polynomials
Permalink:: http://dlmf.nist.gov/18.4.F6
Encodings:: pdf, png

Figure 18.4.7: Monic Hermite polynomials $h_{n}(x)=2^{{-n}}\mathop{H_{{n}}\/}\nolimits\!\left(x\right)$ , $n=1,2,3,4,5$ .

Symbols:: $\mathop{H_{{n}}\/}\nolimits\!\left(x\right)$ : Hermite polynomial, $n$ : nonnegative integer and $x$ : real variable
Keywords:: Hermite polynomials
Referenced by:: §18.2(vi)
Permalink:: http://dlmf.nist.gov/18.4.F7
Encodings:: pdf, png

§18.4(ii) Surfaces

Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/18.4.ii

Visualization Help

Figure 18.4.8: Laguerre polynomials $\mathop{L^{{(\alpha)}}_{{3}}\/}\nolimits\!\left(x\right)$ , $0\leq\alpha\leq 3$ , $0\leq x\leq 10$ .

Symbols:: $\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Laguerre (or generalized Laguerre) polynomial and $x$ : real variable
Permalink:: http://dlmf.nist.gov/18.4.F8
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 18.4.9: Laguerre polynomials $\mathop{L^{{(\alpha)}}_{{4}}\/}\nolimits\!\left(x\right)$ , $0\leq\alpha\leq 3$ , $0\leq x\leq 10$ .

Symbols:: $\mathop{L^{{(\alpha)}}_{{n}}\/}\nolimits\!\left(x\right)$ : Laguerre (or generalized Laguerre) polynomial and $x$ : real variable
Permalink:: http://dlmf.nist.gov/18.4.F9
Encodings:: VRML, X3D, pdf, png

§18.4 Graphics

Contents

§18.4(i) Graphs

§18.4(ii) Surfaces