DLMF:10.38.E1 (Q3560): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.38.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{\partial I_{\pm\nu}\left(z\right)}{\partial% \nu}=\pm I_{\pm\nu}\left(z\right)\ln\left(\tfrac{1}{2}z\right)\mp(\tfrac{1}{2}% z)^{\pm\nu}\sum_{k=0}^{\infty}\frac{\psi\left(k+1\pm\nu\right)}{\Gamma\left(k+% 1\pm\nu\right)}\frac{(\frac{1}{4}z^{2})^{k}}{k!},}}

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DLMF:10.38.E1

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Defining formula

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

C5.S2.E1.m2adec

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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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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2adec

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partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

C1.S5.E3.m4adec

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partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

C1.S5.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1dec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1dec

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Sitelinks

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