Formula:7820

Digital Library of Mathematical Functions ID 22.16.E8

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Jacobiamk@{x}{k}=\Gudermannian@@{x}-\tfrac{1}{4}{k^{\prime}}^{2}(x-\sinh@@{x}\cosh@@{x})\sech@@{x}+\bigO\left({k^{\prime}}^{4}\right).}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}$: Gudermannian function
• ${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s amplitude function
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$: hyperbolic secant function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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