DLMF:13.21.E16 (Q4624): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.21.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{\pi\mathrm{i}}\right)=e^% {-2\mu\pi\mathrm{i}}c(\kappa,\mu)\Psi(\kappa,\mu,x)\left({H^{(2)}_{2\mu}}\left% (\sqrt{\zeta\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(\sqrt{\zeta% \kappa}\right)O\left(\kappa^{-1}\right)\right),}}

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DLMF:13.21.E16

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order not exceeding

Defining formula

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

C2.S1.E3.m2aidec

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Bessel function of the third kind (or Hankel function)

Defining formula

{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

C10.S2.E6.m2aadec

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Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E3.m2afdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar% {x}\right)}}

C2.S8.SS4.p5.m4aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2agdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1ndec

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