DLMF:11.4.E22 (Q3954)

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Language	Label	Description	Also known as
English	DLMF:11.4.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{H}_{1}\left(z\right)=\frac{2}{\pi}(1-J_{0}% \left(z\right))+\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{J_{2k}\left(z\right)}{4k% ^{2}-1}=4\sum_{k=0}^{\infty}J_{2k+\frac{1}{2}}\left(\tfrac{1}{2}z\right)J_{2k+% \frac{3}{2}}\left(\tfrac{1}{2}z\right).}}

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DLMF:11.4.E22

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aedec

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Struve function

Defining formula

{\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C11.S2.E1.m2aldec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2apdec

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Defining formula

{\displaystyle{\displaystyle z}}

C11.S1.XMD2.m1tdec

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Defining formula

{\displaystyle{\displaystyle k}}

C11.S1.XMD5.m1ddec

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