DLMF:10.20.E6 (Q3255): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.20.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\rselection{{H^{(1)}_{\nu}}\left(\nu z\right)\\ {H^{(2)}_{\nu}}\left(\nu z\right)}\sim 2e^{\mp\pi i/3}\left(\frac{4\zeta}{1-z^% {2}}\right)^{\frac{1}{4}}\left(\frac{\mathrm{Ai}\left(e^{\pm 2\pi i/3}\nu^{% \frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\sum_{k=0}^{\infty}\frac{A_{k}(% \zeta)}{\nu^{2k}}+\frac{e^{\pm 2\pi i/3}\mathrm{Ai}'\left(e^{\pm 2\pi i/3}\nu^% {\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}\sum_{k=0}^{\infty}\frac{B_{k}(% \zeta)}{\nu^{2k}}\right),}}

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DLMF:10.20.E6

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Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

C9.S2.SS1.m1aadec

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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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Bessel function of the third kind (or Hankel function)

Defining formula

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

C10.S2.E6.m2adec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11abdec

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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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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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