Formula:9599

Digital Library of Mathematical Functions ID 30.11.E12

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle A_{n}^{-m}(\gamma^{2})\radsphwaveS{m}{1}{n}@{z}{\gamma}=\frac{1}{2}\iunit^{m+n}\gamma^{m}\frac{(n-m)!}{(n+m)!}z^{m}(1-z^{-2})^{\frac{1}{2}m}\*\int_{-1}^{1}e^{-\iunit\gamma zt}(1-t^{2})^{\frac{1}{2}m}\sphwavePsreal{m}{n}@{t}{\gamma^{2}}\diff{t}.}

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},\NVar{\gamma}\right)}}$: radial spheroidal wave function
• ${\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n\geq m}}$: integer degree
• ${\displaystyle{\displaystyle A_{n}^{m}(\gamma^{2})}}$: 30.11.E4
• ${\displaystyle{\displaystyle\gamma^{2}}}$: real parameter
 

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