DLMF:30.11.E6 (Q8901)

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Language	Label	Description	Also known as
English	DLMF:30.11.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle S^{m(j)}_{n}\left(z,\gamma\right)=\begin{cases}% \psi_{n}^{(j)}(\gamma z)+O\left(z^{-2}e^{|\Im z|}\right),&j=1,2,\\ \psi_{n}^{(j)}(\gamma z)\left(1+O\left(z^{-1}\right)\right),&j=3,4.\end{cases}}}

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DLMF:30.11.E6

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2adec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle\Im}}

C1.S9.E2.m2adec

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radial spheroidal wave function

Defining formula

{\displaystyle{\displaystyle S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},% \NVar{\gamma}\right)}}

C30.S11.E3.m2afdec

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Defining formula

{\displaystyle{\displaystyle z}}

C30.S1.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle m}}

C30.S1.XMD4.m1cdec

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Defining formula

{\displaystyle{\displaystyle n\geq m}}

C30.S1.XMD5.m1gdec

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spherical function (locally)

Defining formula

{\displaystyle{\displaystyle\psi_{k}^{(j)}(z)}}

C30.S11.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle\gamma^{2}}}

C30.S2.XMD3.m1cdec

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Sitelinks

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