DLMF:15.9.E14 (Q5104)

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Language	Label	Description	Also known as
English	DLMF:15.9.E14	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\Phi^{(\alpha,\beta)}_{\lambda}(t)=(2\cosh t)^{% \mathrm{i}\lambda-\alpha-\beta-1}F\left({\tfrac{1}{2}(\alpha+\beta+1-\mathrm{i% }\lambda),\tfrac{1}{2}(\alpha-\beta+1-\mathrm{i}\lambda)\atop 1-\mathrm{i}% \lambda};{\operatorname{sech}^{2}}t\right).}}

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DLMF:15.9.E14

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Symbols defined

function (locally)

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$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

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

C15.S2.E1.m2akdec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2aadec

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hyperbolic secant function

Defining formula

{\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

C4.S28.E6.m2adec

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Defining formula

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

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}

introduction.Sx4.p1.t1.r29.m6aadec

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