DLMF:10.22.E61 (Q3435): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E61	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{-1}e^{ibt}J_{\mu}\left(at% \right)\mathrm{d}t=\begin{cases}(1/\mu)\exp\left(i\mu\operatorname{arcsin}% \left(b/a\right)\right),&0\leq b\leq a,\\ \dfrac{a^{\mu}\exp\left(\frac{1}{2}\mu\pi i\right)}{\mu\left(b+(b^{2}-a^{2})^{% \frac{1}{2}}\right)^{\mu}},&0<a\leq b.\end{cases}}}

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DLMF:10.22.E61

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aatdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2axdec

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Defining formula

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

C1.S4.SS4.m1abhdec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aedec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abhdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

C4.S23.SS2.p1.m5abdec

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