DLMF:10.22.E40 (Q3414): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E40	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{x}^{\infty}\frac{Y_{0}\left(t\right)}{t}% \mathrm{d}t=-\frac{1}{\pi}\left(\ln\left(\tfrac{1}{2}x\right)+\gamma\right)^{2% }+\frac{\pi}{6}+\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\*\left(\psi\left(k+1% \right)+\frac{1}{2k}-\ln\left(\tfrac{1}{2}x\right)\right)\frac{(\tfrac{1}{2}x)% ^{2k}}{2k(k!)^{2}},}}

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DLMF:10.22.E40

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2acdec

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Euler’s constant

Defining formula

{\displaystyle{\displaystyle\gamma}}

C5.S2.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.m2aodec

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Defining formula

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

C1.S4.SS4.m1aamdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aamdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2aadec

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Sitelinks

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