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Fast computation of complete elliptic integrals and Jacobian elliptic functions
Celestial Mechanics and Dynamical Astronomy, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toshio Fukushima
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Integrals associated with Ramanujan and elliptic functions
The Ramanujan Journal, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Elliptic integrals, theta functions and elliptic functions
1966General remarks. Any integral of the type ∫ R \(\left( {z,{Z^{\frac{1}{2}}}} \right)\) is a rational function of x and y and Z is a polynomial of the third or fourth degree in z with real coefficients and no repeated factors is called an elliptic integral.
Wilhelm Magnus +2 more
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Equivariant functions and integrals of elliptic functions
Geometriae Dedicata, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sebbar, Abdellah, Sebbar, Ahmed
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Numerical calculation of elliptic integrals and elliptic functions
Numerische Mathematik, 1965Methoden (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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On Computing Elliptic Integrals and Functions
Journal of Mathematics and Physics, 1965Elliptic integral and function direct computation method using successive quadratic Landen and Gauss ...
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Generalized Grötzsch ring function and generalized elliptic integrals
Applied Mathematics-A Journal of Chinese Universities, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Xiaoyan, Qiu, Songliang, Tu, Guoyan
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Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions
Physical Review E, 1993We show that the generating function for d-dimensional staircase polygons (by perimeter) can be expressed in terms of the generating function for the square of d-dimensional multinomial coefficients. This latter generating function is found to satisfy a linear, homogeneous differential equation of order d-1. This equation is solved for d\ensuremath{\le}
, Guttmann, , Prellberg
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Elliptic functions and integrals
2011Abstract This chapter examines Riemann surfaces of genus 1. The constructions give an important model for the more general theory to be developed in Part III. The constructions also involve classical topics in mathematics, which relate the abstractions of Riemann surface theory to their origin in concrete calculus problems.
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Fractional power approximations of elliptic integrals and bessel functions
Mathematics and Computers in Simulation, 1978Abstract In the previous papers [1]∽[3], fractional powers were used to approximate elementary functions and their usefulness was proved with experimental results. In the present paper, some further investigations are reported. That is, elliptic integrals in Legendre's canonical form and Bessel functions are approximated by fractional powers.
Kobayashi, Yasuhiro +2 more
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