DLMF:12.12.E4 (Q4229)

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Language	Label	Description	Also known as
English	DLMF:12.12.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(U\left(a,z\right))^{2}+(\overline{U}\left(a,z% \right))^{2}=\frac{2^{\frac{3}{2}}}{\pi}\Gamma\left(\tfrac{1}{2}-a\right)\int_% {0}^{\infty}\frac{e^{2at+\frac{1}{2}z^{2}\tanh t}}{\sqrt{\sinh\left(2t\right)}% }\mathrm{d}t,}}

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DLMF:12.12.E4

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{\displaystyle{\displaystyle\Re a<\tfrac{1}{2}}}

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Defining formula

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

C5.S2.E1.m2acdec

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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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Defining formula

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

C1.S4.SS4.m1acdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2acdec

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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2adec

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hyperbolic tangent function

Defining formula

{\displaystyle{\displaystyle\tanh\NVar{z}}}

C4.S28.E4.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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Defining formula

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

C12.S2.SS1.p1.m1acdec

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Defining formula

{\displaystyle{\displaystyle\overline{U}\left(\NVar{a},\NVar{x}\right)}}

C12.S2.SS6.p1.m4adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1acdec

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Sitelinks

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DRMF related sites(0 entries)

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