Erdal Imamoglu
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View article: HERMITE INTERPOLATION WITH DICKSON POLYNOMIALS AND BERNSTEIN BASIS POLYNOMIALS
HERMITE INTERPOLATION WITH DICKSON POLYNOMIALS AND BERNSTEIN BASIS POLYNOMIALS Open
In this manuscript we introduce three new algorithms: (1) An algorithm to recover an unknown polynomial in terms of Dickson polynomials of the first kind, (2) an algorithm to recover an unknown polynomial in terms Dickson polynomials of th…
View article: AN ALGORITHM TO COMPUTE THE DEGREE OF A DICKSON POLYNOMIAL
AN ALGORITHM TO COMPUTE THE DEGREE OF A DICKSON POLYNOMIAL Open
In this study, we describe an algorithm that computes the degree of a Dickson Polynomial of the First Kind from its known value at a point. Our algorithm is based on a mathematical relation between Dickson Polynomials of the First Kind and…
View article: Sparse polynomial interpolation with Bernstein polynomials
Sparse polynomial interpolation with Bernstein polynomials Open
We present an algorithm for interpolating an unknown univariate polynomial f that has a t sparse representation ( t << deg(f ) ) using Bernstein polynomials as term basis from 2t evaluations.Our method is based on manipulating given black …
View article: A note on sparse polynomial interpolation in Dickson polynomial basis
A note on sparse polynomial interpolation in Dickson polynomial basis Open
research-article A note on sparse polynomial interpolation in Dickson polynomial basis Share on Authors: Erdal Imamoglu Kirklareli University, Kirklareli, Turkey Kirklareli University, Kirklareli, TurkeyView Profile , Erich L. Kaltofen Nor…
View article: The ρ parameter at three loops and elliptic integrals
The ρ parameter at three loops and elliptic integrals Open
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding dif…
View article: Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases
Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases Open
An algorithm for interpolating a polynomial f from evaluation points whose running time depends on the sparsity t of the polynomial when it is represented as a sum of t Chebyshev Polynomials of the First Kind with non-zero scalar coefficie…
View article: Iterated elliptic and hypergeometric integrals for Feynman diagrams
Iterated elliptic and hypergeometric integrals for Feynman diagrams Open
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop quantum chromodynamics corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, whi…
View article: The $\rho$ parameter at three loops and elliptic integrals
The $\rho$ parameter at three loops and elliptic integrals Open
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding dif…
View article: Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations
Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations Open
Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the an…
View article: Computing Hypergeometric Solutions of Second Order Linear Differential\n Equations using Quotients of Formal Solutions and Integral Bases
Computing Hypergeometric Solutions of Second Order Linear Differential\n Equations using Quotients of Formal Solutions and Integral Bases Open
We present two algorithms for computing hypergeometric solutions of second\norder linear differential operators with rational function coefficients. Our\nfirst algorithm searches for solutions of the form \\[ \\exp(\\int r \\,\ndx)\\cdot{_…