DLMF:13.21.E2 (Q4610)

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Language	Label	Description	Also known as
English	DLMF:13.21.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{x}\Gamma\left(% \kappa+\tfrac{1}{2}\right)\*\left(\sin\left(\kappa\pi-\mu\pi\right)J_{2\mu}% \left(2\sqrt{x\kappa}\right)-\cos\left(\kappa\pi-\mu\pi\right)Y_{2\mu}\left(2% \sqrt{x\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(2\sqrt{x\kappa}% \right)O\left(\kappa^{-\frac{1}{2}}\right)\right),}}

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DLMF:13.21.E2

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2aadec

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Bessel function of the second kind

Defining formula

{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E3.m2adec

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order not exceeding

Defining formula

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

C2.S1.E3.m2aadec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.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.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2adec

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Defining formula

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

C2.S8.SS4.p5.m4adec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1adec

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