DLMF:15.12.E5 (Q5165)

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Language	Label	Description	Also known as
English	DLMF:15.12.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left({a+\lambda,b-\lambda\atop c};% \tfrac{1}{2}-\tfrac{1}{2}z\right)=2^{(a+b-1)/2}\frac{(z+1)^{(c-a-b-1)/2}}{(z-1% )^{c/2}}\sqrt{\zeta\sinh\zeta}\left(\lambda+\tfrac{1}{2}a-\tfrac{1}{2}b\right)% ^{1-c}\left(I_{c-1}\left((\lambda+\tfrac{1}{2}a-\tfrac{1}{2}b)\zeta\right)(1+O% (\lambda^{-2}))+\frac{I_{c-2}\left((\lambda+\tfrac{1}{2}a-\tfrac{1}{2}b)\zeta% \right)}{2\lambda+a-b}\left(\left(c-\tfrac{1}{2}\right)\left(c-\tfrac{3}{2}% \right)\left(\frac{1}{\zeta}-\coth\zeta\right)+\tfrac{1}{2}(2c-a-b-1)(a+b-1)% \tanh\left(\tfrac{1}{2}\zeta\right)+O(\lambda^{-2})\right)\right),}}

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DLMF:15.12.E5

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.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.m2adec

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hyperbolic tangent function

Defining formula

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

C4.S28.E4.m2adec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ddec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1cdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1cdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1cdec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C15.S12.XMD5.m1dec

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Sitelinks

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