DLMF:28.23.E5 (Q8389)

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Language	Label	Description	Also known as
English	DLMF:28.23.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{me}_{\nu}'\left(\tfrac{1}{2}\pi,h^{2}% \right){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)=\mathrm{i}e^{\mathrm{i}\nu% \ifrac{\pi}{2}}\coth z\sum_{n=-\infty}^{\infty}(\nu+2n)c_{2n}^{\nu}(h^{2}){% \cal C}_{\nu+2n}^{(j)}(2h\sinh z),}}

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DLMF:28.23.E5

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Defining formula

{\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

C28.S12.SS2.p2.m2acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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hyperbolic cotangent function

Defining formula

{\displaystyle{\displaystyle\coth\NVar{z}}}

C4.S28.E7.m2adec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2aadec

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Defining formula

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

C1.S9.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

C28.S20.SS3.p1.m4acdec

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Defining formula

{\displaystyle{\displaystyle h}}

C28.S1.XMD11.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C28.S1.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle j}}

C28.S1.XMD3.m1ddec

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Defining formula

{\displaystyle{\displaystyle z}}

C28.S1.XMD6.m1cdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C28.S1.XMD7.m1cdec

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Defining formula

{\displaystyle{\displaystyle c_{2m}(q)}}

C28.S14.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}

C28.S23.XMD1.m1ddec

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