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Coupling coefficients of suq(1,1) and multivariate q-Racah polynomials
Nuclear Physics B, 2018 Gasper & Rahman's multivariate q-Racah polynomials are shown to arise as connection coefficients between families of multivariate q-Hahn or q-Jacobi polynomials. The families of q-Hahn polynomials are constructed as nested Clebsch–Gordan coefficients
Vincent X. Genest +2 more
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On Triple Series Equations Involving Series of Jacobi Polynomials [PDF]
, 1967 S.C. Srivastava
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Jacobi polynomials in Bernstein form
Journal of Computational and Applied Mathematics, 2007 AbstractThe paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so-called Bernstein–Bézier form of a polynomial.
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Darboux transformation of symmetric Jacobi matrices and Toda lattices
Frontiers in Applied Mathematics and StatisticsLet J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
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Extreme eigen values of Toeplitz forms associated with Jacobi polynomials [PDF]
, 1964 I. I. Hirschman
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On the maximum value of Jacobi polynomials
Journal of Approximation Theory, 2005 AbstractA remarkable inequality, with utterly explicit constants, established by Erdélyi, Magnus, and Nevai, states that for α⩾β>-12, the orthonormal Jacobi polynomials Pk(α,β)(x) satisfymax|x|⩽1(1-x)α+1/2(1+x)β+1/2Pk(α,β)(x)2=O(α)[Erdélyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal.
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Finite Integral Formulas Involving Multivariable Aleph-Functions
Journal of Applied Mathematics, 2019 The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials.
Hagos Tadesse +2 more
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Some triple series equations involving Jacobi polynomials [PDF]
, 1968 J. S. Lowndes
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The orthogonal polynomials generated by [ceteris omissis] [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1995 Starting from the generating function, a differential-recurrence relation is derived, which is then combined with the three-term pure recurrence formula (a necessary and sufficient condition for orthogonal polynomials) to obtain a differential ...
A.L.W. VON BACHHAUS
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