DLMF:28.28.E41 (Q8472)

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Language	Label	Description	Also known as
English	DLMF:28.28.E41	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\dfrac{\cosh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin t% \mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)}{{\sinh% ^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p+1}\mathrm{i}h\widehat{\beta}_{n,m}% \mathrm{Dsc}_{0}\left(n,m,z\right),}}

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DLMF:28.28.E41

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Defining formula

{\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},% \NVar{z}\right)}}

C28.S28.E40.m1aadec

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Defining formula

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

C28.S2.SS6.p1.m7agdec

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Defining formula

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

C28.S2.SS6.p1.m8ahdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aagdec

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Defining formula

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

C1.S4.SS4.m1aaedec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2amdec

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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2akdec

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Defining formula

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

C1.S9.E1.m2aaadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aaddec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2andec

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Defining formula

{\displaystyle{\displaystyle m}}

C28.S1.XMD1.m1vdec

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Defining formula

{\displaystyle{\displaystyle h}}

C28.S1.XMD11.m1ajdec

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Defining formula

{\displaystyle{\displaystyle n}}

C28.S1.XMD2.m1ldec

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Defining formula

{\displaystyle{\displaystyle z}}

C28.S1.XMD6.m1afdec

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Defining formula

{\displaystyle{\displaystyle\widehat{\beta}_{n,m}}}

C28.S28.XMD9.m1dec

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Sitelinks

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