Formula:9315

Digital Library of Mathematical Functions ID 29.5.E5

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle {\lim_{k\to 1-}\frac{\LameEc{m}{\nu}@{z}{k^{2}}}{\LameEc{m}{\nu}@{0}{k^{2}}}=\lim_{k\to 1-}\frac{\LameEs{m+1}{\nu}@{z}{k^{2}}}{\LameEs{m+1}{\nu}@{0}{k^{2}}}}=\frac{1}{(\cosh@@{z})^{\mu}}\hyperF@@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}{\tfrac{1}{2}}{\tanh^{2}@@{z}},}

Constraint(s)

${\displaystyle{\displaystyle m}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},\NVar{k^{2}}\right)}}$:
• ${\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},\NVar{k^{2}}\right)}}$:
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle k}}$: real parameter
• ${\displaystyle{\displaystyle\nu}}$: real parameter
• ${\displaystyle{\displaystyle\mu}}$: parameter
 

Resources that cite this formula

No records found.