DLMF:10.43.E5 (Q3619): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.43.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{x}^{\infty}\frac{K_{0}\left(t\right)}{t}% \mathrm{d}t=\frac{1}{2}\left(\ln\left(\tfrac{1}{2}x\right)+\gamma\right)^{2}+% \frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\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:10.43.E5

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Euler’s constant

Defining formula

{\displaystyle{\displaystyle\gamma}}

C5.S2.E3.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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Defining formula

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

C1.S4.SS4.m1addec

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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!}}

introduction.Sx4.p1.t1.r15.m5aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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modified Bessel function of the second kind

Defining formula

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

C10.S25.E3.m2adec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1adec

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Sitelinks

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