DLMF:13.10.E12 (Q4471): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.10.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(2xt\right){\mathbf{M}}% \left(a,b,-t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{2\Gamma\left(a\right)}x^{% 2a-1}e^{-x^{2}}U\left(b-\tfrac{1}{2},a+\tfrac{1}{2},x^{2}\right),}}

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DLMF:13.10.E12

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

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Defining formula

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

C5.S2.E1.m2ahdec

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Kummer confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

C13.S2.E6.m2aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2adec

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Defining formula

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

C1.S4.SS4.m1akdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2agdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3akdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aidec

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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.m2agdec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1dec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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