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RATIONAL LANDEN TRANSFORMATIONS ON R
, 2007
"... The Landen transformation (a, b) ↦ → ((a+b)/2, √ab) preserves the value of an elliptic integral, and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line. ..."
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The Landen transformation (a, b) ↦ → ((a+b)/2, √ab) preserves the value of an elliptic integral, and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line.
Landen transformation and the integration of rational functions
 MATH. COMP
, 2001
"... We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closedform expressions for a large class of integrals of even rational functions and to develop an algorithm for numerical integration of these functions. ..."
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Cited by 11 (5 self)
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We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closedform expressions for a large class of integrals of even rational functions and to develop an algorithm for numerical integration of these functions.
A GEOMETRIC VIEW OF RATIONAL LANDEN Transformations
, 2003
"... In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established. 1 ..."
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Cited by 13 (6 self)
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In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established. 1
Generalized Landen Transformation Formulas for Jacobi Elliptic Functions
, 2003
"... Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals. We rediscover known results as well as obtain more generalized Landen formulas from a ver ..."
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Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals. We rediscover known results as well as obtain more generalized Landen formulas from a
Dynamics of the degree six Landen transformation
 Discrete and Dynamical Systems
"... Abstract. We establish the basin of attraction for the fixed point (3, 3) of a dynamical system arising from the evaluation of a definite integral. 1. ..."
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Cited by 6 (2 self)
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Abstract. We establish the basin of attraction for the fixed point (3, 3) of a dynamical system arising from the evaluation of a definite integral. 1.
Arational Landen transformation. The case of degree six
 Contemp. Math
"... Abstract. We prove the existence of a Landentype transformation for the integral of a rational function. The convergence of its iterates is established. 1. ..."
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Cited by 14 (8 self)
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Abstract. We prove the existence of a Landentype transformation for the integral of a rational function. The convergence of its iterates is established. 1.
LANDEN TRANSFORMS AS FAMILIES OF (COMMUTING) RATIONAL SELFMAPS OF PROJECTIVE SPACE
, 2013
"... The classical (m, k)Landen transform Fm,k is a selfmap of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m’th roots of unity. Identifying the set of rational maps of degree d with an affine open subset of P2d+1, we prove that Fm,0 ..."
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The classical (m, k)Landen transform Fm,k is a selfmap of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m’th roots of unity. Identifying the set of rational maps of degree d with an affine open subset of P2d+1, we prove that Fm
THE DERIVATION OF ALGORITHMS TO COMPUTE ELLIPTIC INTEGRALS OF THE FIRST AND SECOND KIND BY LANDENTRANSFORMATION
"... Desenvolvimento de algoritmos para o cálculo de integrais elípticas de primeira e segunda ordens por meio da Ttransformação de Landen ..."
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Desenvolvimento de algoritmos para o cálculo de integrais elípticas de primeira e segunda ordens por meio da Ttransformação de Landen
A simple example of a new class of Landen transformations
 American Mathematical Montly
, 2006
"... procedure to evaluate dx ..."
Landen Survey
"... To Henry, who provides inspiration, taste and friendship ABSTRACT. Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearance in the literature. 1. In the beginning there was Gauss In the year 1985, one of us had the luxu ..."
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Cited by 2 (2 self)
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To Henry, who provides inspiration, taste and friendship ABSTRACT. Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearance in the literature. 1. In the beginning there was Gauss In the year 1985, one of us had
Results 1  10
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1,420