DLMF:10.19.E13 (Q3240): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.19.E13	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{5}{3}}% }{\nu^{\frac{2}{3}}}e^{\pm\pi i/3}\mathrm{Ai}'\left(e^{\mp\pi i/3}2^{\frac{1}{% 3}}a\right)\sum_{k=0}^{\infty}\frac{R_{k}(a)}{\nu^{2k/3}}+\frac{2^{\frac{4}{3}% }}{\nu^{\frac{4}{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{S_{k}(a)}{\nu^{2k/3}},}}

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DLMF:10.19.E13

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Defining formula

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

C9.S2.SS1.m1acdec

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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.m2abdec

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11agdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ajdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aedec

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Defining formula

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

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1gdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1jdec

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Defining formula

{\displaystyle{\displaystyle R_{k}(a)}}

C10.S19.XMD3.m1adec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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