DLMF:13.21.E3 (Q4611): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.21.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=% \frac{\pi\sqrt{x}}{\Gamma\left(\kappa+\tfrac{1}{2}\right)}e^{\mu\pi\mathrm{i}}% \*\left({H^{(1)}_{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.E3

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order not exceeding

Defining formula

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

C2.S1.E3.m2abdec

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Defining formula

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

C5.S2.E1.m2abdec

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Bessel function of the third kind (or Hankel function)

Defining formula

{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

C10.S2.E5.m2adec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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Defining formula

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

C2.S8.SS4.p5.m4aadec

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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\mathrm{i}}}

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1bdec

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