DLMF:10.31.E1 (Q3518): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.31.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle K_{n}\left(z\right)=\tfrac{1}{2}(\tfrac{1}{2}z)^{% -n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}(-\tfrac{1}{4}z^{2})^{k}+(-1)^{n+1}\ln% \left(\tfrac{1}{2}z\right)I_{n}\left(z\right)+(-1)^{n}\tfrac{1}{2}(\tfrac{1}{2% }z)^{n}\sum_{k=0}^{\infty}\left(\psi\left(k+1\right)+\psi\left(n+k+1\right)% \right)\frac{(\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!},}}

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DLMF:10.31.E1

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

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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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Sitelinks

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