DLMF:12.13.E5 (Q4234): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:12.13.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,x\cos t+y\sin t\right)\\ =e^{\frac{1}{4}(x\sin t-y\cos t)^{2}}\*\sum_{m=0}^{\infty}\genfrac{(}{)}{0.0pt% }{}{-a-\tfrac{1}{2}}{m}(\tan t)^{m}U\left(m+a,x\right)U\left(-m-\tfrac{1}{2},y% \right),}}

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DLMF:12.13.E5

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{\displaystyle{\displaystyle\Re a\leq-\tfrac{1}{2},0\leq t\leq\tfrac{1}{4}\pi}}

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

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

C12.S2.SS1.p1.m1abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

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

C4.S14.E1.m2adec

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tangent function

Defining formula

{\displaystyle{\displaystyle\tan\NVar{z}}}

C4.S14.E4.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C12.S1.XMD1.m1ddec

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Defining formula

{\displaystyle{\displaystyle y}}

C12.S1.XMD2.m1ddec

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Sitelinks

Wikipedia(0 entries)

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