DLMF:13.4.E3 (Q4366): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.4.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{z^{\frac{1}{% 2}-\frac{1}{2}b}}{\Gamma\left(a\right)}\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}% b-\frac{1}{2}}J_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t,}}

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DLMF:13.4.E3

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{\displaystyle{\displaystyle\Re a>0}}

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

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Defining formula

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

C5.S2.E1.m2abdec

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Olver’s confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}

C13.S2.E3.m2abdec

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Defining formula

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

C1.S4.SS4.m1abdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1abdec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1bdec

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