DLMF:10.22.E12 (Q3386): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle x\int_{0}^{x}\frac{1-J_{0}\left(t\right)}{t}% \mathrm{d}t=2\sum_{k=0}^{\infty}(2k+3)(\psi\left(k+2\right)-\psi\left(1\right)% )J_{2k+3}\left(x\right)=x-2J_{1}\left(x\right)+2\sum_{k=0}^{\infty}(2k+5)\*(% \psi\left(k+3\right)-\psi\left(1\right)-1)J_{2k+5}\left(x\right),}}

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DLMF:10.22.E12

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1akdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3akdec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1ddec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1ddec

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Sitelinks

Wikipedia(0 entries)

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