DLMF:10.19.E9 (Q3228)

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Language	Label	Description	Also known as
English	DLMF:10.19.E9	No description defined

Statements

Defining formula

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

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DLMF:10.19.E9

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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.m2aadec

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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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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11aedec

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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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