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Elliptic Integrals

Special Functions in Physics with MATLAB, 2021
W. Schweizer
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A concavity property of generalized complete elliptic integrals

, 2020
We prove that, for and , the function is strictly concave on if and only if where represents the generalized complete p-elliptic integrals of the first kind defined by where , , and is the generalized sine function, with This extends the recently ...
Kendall C. Richards, Jordan N. Smith
semanticscholar   +1 more source

Monotonicity properties of generalized elliptic integrals with respect to the parameter

, 2020
For a ∈ ( 0 , 1 / 2 ] and r ∈ ( 0 , 1 ) , let K a ( r ) and E a ( r ) ( K ( r ) and E ( r ) ) denote the generalized elliptic integrals (the complete elliptic integrals, respectively) of the first and second kinds, respectively.
S. Qiu, Xiao-Yan Ma, Qi Bao
semanticscholar   +1 more source

Integrable elliptic pseudopotentials

Theoretical and Mathematical Physics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Odesskii, A. V., Sokolov, V. V.
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Numerical calculation of elliptic integrals and elliptic functions

Numerische Mathematik, 1965
Methoden (unter Benutzung der Landen- und Gauß-Transformation) und ALGOL 60-Programme zur Berechnung elliptischer Integrale 1., 2. und 3. Art für reelles Argument und 1. und 2. Art für komplexes Argument, wobei auf möglichst rasche Berechnung im Bereich \(0.001\leq k' \leq 1000\) Wert gelegt wird.
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Elliptic Integral Inequalities, with Applications

Constructive Approximation, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anderson, G. D.   +2 more
openaire   +1 more source

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