§30.7 Graphics

§30.7(i) Eigenvalues

Notes:: Figures 30.7.1–30.7.4 were produced at NIST with the aid of Maple procedures provided by the author.
Keywords:: spheroidal differential equation
Permalink:: http://dlmf.nist.gov/30.7.i

Figure 30.7.1: Eigenvalues $\mathop{\lambda^{{0}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ , $n=0,1,2,3$ , $-10\leq\gamma^{2}\leq 10$ .

Symbols:: $\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(i)
Permalink:: http://dlmf.nist.gov/30.7.F1
Encodings:: pdf, png

Figure 30.7.2: Eigenvalues $\mathop{\lambda^{{1}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ $n=1,2,3,4$ , $-10\leq\gamma^{2}\leq 10$ .

Symbols:: $\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F2
Encodings:: pdf, png

Figure 30.7.3: Eigenvalues $\mathop{\lambda^{{5}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ , $n=5,6,7,8$ , $-40\leq\gamma^{2}\leq 40$ .

Symbols:: $\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F3
Encodings:: pdf, png

Figure 30.7.4: Eigenvalues $\mathop{\lambda^{{10}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ , $n=10,11,12,13$ , $-50\leq\gamma^{2}\leq 150$ .

Symbols:: $\mathop{\lambda^{{m}}_{{n}}\/}\nolimits\!\left(\gamma^{2}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(i)
Permalink:: http://dlmf.nist.gov/30.7.F4
Encodings:: pdf, png

Notes:: Figures 30.7.5–30.7.10 were produced at NIST with the aid of Maple procedures provided by the author.
Keywords:: spheroidal wave functions
Permalink:: http://dlmf.nist.gov/30.7.ii

Figure 30.7.5: $\mathop{\mathsf{Ps}^{{0}}_{{n}}\/}\nolimits\!\left(x,4\right)$ , $n=0,1,2,3$ , $-1\leq x\leq 1$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $n\geq m$ : integer degree
Referenced by:: §30.7(ii)
Permalink:: http://dlmf.nist.gov/30.7.F5
Encodings:: pdf, png

Figure 30.7.6: $\mathop{\mathsf{Ps}^{{0}}_{{n}}\/}\nolimits\!\left(x,-4\right)$ , $n=0,1,2,3$ , $-1\leq x\leq 1$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F6
Encodings:: pdf, png

Figure 30.7.7: $\mathop{\mathsf{Ps}^{{1}}_{{n}}\/}\nolimits\!\left(x,30\right)$ , $n=1,2,3,4$ , $-1\leq x\leq 1$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F7
Encodings:: pdf, png

Figure 30.7.8: $\mathop{\mathsf{Ps}^{{1}}_{{n}}\/}\nolimits\!\left(x,-30\right)$ , $n=1,2,3,4$ , $-1\leq x\leq 1$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F8
Encodings:: pdf, png

Figure 30.7.9: $\mathop{\mathsf{Ps}^{{0}}_{{2}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ , $-1\leq x\leq 1$ , $-50\leq\gamma^{2}\leq 50$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F9
Encodings:: VRML, X3D, pdf, png

Figure 30.7.10: $\mathop{\mathsf{Ps}^{{1}}_{{3}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ , $-1\leq x\leq 1$ , $-50\leq\gamma^{2}\leq 50$ .

Symbols:: $\mathop{\mathsf{Ps}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the first kind, $x$ : real variable and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(ii)
Permalink:: http://dlmf.nist.gov/30.7.F10
Encodings:: VRML, X3D, pdf, png

Notes:: Figures 30.7.11–30.7.15 were produced at NIST with the aid of Maple procedures provided by the author.
Permalink:: http://dlmf.nist.gov/30.7.iii

Figure 30.7.11: $\mathop{\mathsf{Qs}^{{0}}_{{n}}\/}\nolimits\!\left(x,4\right)$ , $n=0,1,2,3$ , $-1<x<1$ .

Symbols:: $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind, $x$ : real variable and $n\geq m$ : integer degree
Referenced by:: §30.7(iii)
Permalink:: http://dlmf.nist.gov/30.7.F11
Encodings:: pdf, png

Figure 30.7.12: $\mathop{\mathsf{Qs}^{{0}}_{{n}}\/}\nolimits\!\left(x,-4\right)$ , $n=0,1,2,3$ , $-1<x<1$ .

Symbols:: $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F12
Encodings:: pdf, png

Figure 30.7.13: $\mathop{\mathsf{Qs}^{{1}}_{{n}}\/}\nolimits\!\left(x,4\right)$ , for $n=1,2,3,4$ , $-1<x<1$ .

Symbols:: $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F13
Encodings:: pdf, png

Figure 30.7.14: $\mathop{\mathsf{Qs}^{{1}}_{{n}}\/}\nolimits\!\left(x,-4\right)$ , $n=1,2,3,4$ , $-1<x<1$ .

Symbols:: $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind, $x$ : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F14
Encodings:: pdf, png

Figure 30.7.15: $\mathop{\mathsf{Qs}^{{0}}_{{1}}\/}\nolimits\!\left(x,\gamma^{2}\right),-1<x<1,-10\leq\gamma^{2}\leq 10$ .

Symbols:: $\mathop{\mathsf{Qs}^{{m}}_{{n}}\/}\nolimits\!\left(x,\gamma^{2}\right)$ : spheroidal wave function of the second kind, $x$ : real variable and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(iii)
Permalink:: http://dlmf.nist.gov/30.7.F15
Encodings:: VRML, X3D, pdf, png

Notes:: Figures 30.7.16–30.7.21 were produced at NIST with the aid of Maple procedures provided by the author.
Keywords:: spheroidal wave functions
Referenced by:: §30.1
Permalink:: http://dlmf.nist.gov/30.7.iv