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9,448
Rational Summation of Rational Functions
"... In this article we characterize rational functions for which their indefinite sum is again a rational function. 1 Introduction Let k be a eld of characteristic 0 and let r be a rational function in one variable over k. Pick an integer j 0 such that r(j) is dened for j j 0 , and consider y x = x ..."
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In this article we characterize rational functions for which their indefinite sum is again a rational function. 1 Introduction Let k be a eld of characteristic 0 and let r be a rational function in one variable over k. Pick an integer j 0 such that r(j) is dened for j j 0 , and consider y x = x
The use of rational functions in numerical quadrature
- J. Comput. Appl. Math. 133(1-2
"... The use of rational functions in numerical quadrature ..."
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Cited by 3 (0 self)
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The use of rational functions in numerical quadrature
Compositional Representation of Rational Functions
, 1990
"... The rational functions are shown to coincide with the compositions of endmarkings, morphisms and inverses of injective morphisms. To represent a rational function τ we need one endmarking µm, two morphisms α1, α3 and one inverse of an injective morphism α2 and then τ = µmα1α −1 2 α3. ..."
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Cited by 1 (0 self)
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The rational functions are shown to coincide with the compositions of endmarkings, morphisms and inverses of injective morphisms. To represent a rational function τ we need one endmarking µm, two morphisms α1, α3 and one inverse of an injective morphism α2 and then τ = µmα1α −1 2 α3.
On the structure of compatible rational functions
, 2011
"... A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us ..."
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Cited by 2 (2 self)
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A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us
PERMUTABLE POLYNOMIALS AND RATIONAL FUNCTIONS
, 2007
"... Summary. Many infinite sequences of permutable rational functions and a few infinite sequences of permutable polynomials are constructed, on the basis of elliptic functions and trigonometric functions. ..."
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Summary. Many infinite sequences of permutable rational functions and a few infinite sequences of permutable polynomials are constructed, on the basis of elliptic functions and trigonometric functions.
recurrence relation for orthogonal rational functions
"... Associated rational functions based on a three-term ..."
Computing Determinants of Rational Functions ∗
"... Computation of determinants of rational functions seems to be out of thought in computer algebra so far. We first show that representing the rational function by the sum of partial fractions is absolutely necessary in the computation. We then propose a very simple technique for efficient computation ..."
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Computation of determinants of rational functions seems to be out of thought in computer algebra so far. We first show that representing the rational function by the sum of partial fractions is absolutely necessary in the computation. We then propose a very simple technique for efficient
methods for orthogonal rational functions
- J. Comput. Analysis
"... An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication operator associated with the corresponding orthogonality me ..."
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Cited by 7 (0 self)
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An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication operator associated with the corresponding orthogonality
Positivity of rational functions and their diagonals
- JOURNAL OF APPROXIMATION THEORY
, 2013
"... The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szegö as well as Askey and Gasper, who inspired more recent work. It is well known that the diagonal coefficients of rational functions ..."
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Cited by 1 (1 self)
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The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szegö as well as Askey and Gasper, who inspired more recent work. It is well known that the diagonal coefficients of rational
Results 1 - 10
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9,448
