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01/2019, ISBN 9783039216215
.... Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials... 
eBook
Journal of Mathematical Physics, ISSN 1089-7658, 2011, Volume 52, Issue 10, pp. 102301 - 102301-52
... generated as real representations by Mellin transforms of Poincaré–iterated integrals, including denominators of higher cyclotomic polynomials... 
ANALYTIC CONTINUATION | polynomials | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | ALGEBRAIC RELATIONS | HYPERGEOMETRIC-FUNCTIONS | integral equations | harmonics | perturbation theory | ONE-LOOP | renormalisation | MELLIN TRANSFORMS | LEGENDRE CHI | Feynman diagrams | MULTIPLE ZETA VALUES | NESTED SUMS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2017, Volume 322, pp. 25 - 45
.... To obtain highly accurate result for European call option, the implementation involves integrating high degree Legendre polynomials against exponential function... 
Characteristic function | European option pricing | Legendre polynomials | Fourier series | Olver algorithm | MATHEMATICS, APPLIED | SERIES | Analysis | Pricing | Algorithms
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2011, Volume 139, Issue 6, pp. 1915 - 1929
Let p be an odd prime. In this paper, by using the properties of Legendre polynomials we prove some congruences for $\sum\nolimits_{k = 0}^{\frac{{p - 1}}{2}} {{{(_k^{2k})}^2}{m^{ - k}}}$ (m odp₂... 
Integers | Mathematical congruence | Legendre polynomials | Number theory | Legendre polynomial | Congruence | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | HYPERGEOMETRIC-SERIES | SUPERCONGRUENCES | congruence | Mathematics - Number Theory
Journal Article
Annals of physics, ISSN 0003-4916, 2013, Volume 335, pp. 78 - 85
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2015, Volume 84, Issue 293, pp. 1317 - 1337
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2019, Volume 88, Issue 319, pp. 2351 - 2381
We present a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence \{P_k(x)\}_{k \geqslant 0} with \deg P_k(x) = k... 
Jacobi polynomials | MATHEMATICS, APPLIED | Gegenbauer polynomials | Convolution | Laguerre polynomials | REPRESENTATIONS | Volterra convolution integral | CONNECTION COEFFICIENTS | Legendre polynomials | Chebyshev polynomials | orthogonal polynomials
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2018, Volume 12, Issue 2, pp. 362 - 388
Journal Article
SIAM journal on scientific computing, ISSN 1095-7197, 2018, Volume 40, Issue 4, pp. A2336 - A2355
We develop a unified framework for constructing matrix approximations to the convolution operator of Volterra type defined by functions that are approximated using classical orthogonal polynomials on [-1,1... 
Jacobi polynomials | Operator approximation | Gegenbauer polynomials | Convolution | Laguerre polynomials | Volterra convolution integral | Orthogonal polynomials | Legendre polynomials | Ultraspherical polynomials | Chebyshev polynomials | Spectral methods | MATHEMATICS, APPLIED | spectral methods | ALGORITHM | ultraspherical polynomials | convolution | operator approximation | orthogonal polynomials
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 1, pp. 626 - 645
SIAM J. Math. Anal. 49 (2017), no. 1, 626-645 We show that the multiwavelets, introduced by Alpert in 1993, are related to type I Legendre-Angelesco multiple orthogonal polynomials... 
Hypergeometric functions | Alpert multiwavelets | Legendre polynomials | Legendre-Angelesco polynomials | Mathematics - Classical Analysis and ODEs
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 11/2014, Volume 83, Issue 290, pp. 2893 - 2914
Journal Article
Journal of number theory, ISSN 0022-314X, 2013, Volume 133, Issue 6, pp. 1950 - 1976
...). In particular, we show that ∑k=0p−12(2kk)3≡0(modp2) for p≡3,5,6(mod7). Let {Pn(x)} be the Legendre polynomials... 
Binary quadratic form | Congruence | Character sum | Elliptic curve | Legendre polynomial | Legendre p-lynomial | Ellip-ic curve | ELLIPTIC-CURVES | BINOMIAL COEFFICIENTS | CHARACTER SUMS | HYPERGEOMETRIC-SERIES | MATHEMATICS | APERY NUMBERS | SUPERCONGRUENCES | COMPLEX MULTIPLICATION
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 01/2017, Volume 24, Issue 1
.... Kontsevich i i cve conjectured in 1997 that the number of nonzero values of s(alpha, G) is a polynomial in q for all graphs... 
Feynman amplitudes | Laplacian matrix | Flow polynomial | Kontsevich’s conjecture | Tutte 5-flow conjecture | Legendre symbol | MATHEMATICS | MATHEMATICS, APPLIED | flow polynomial | Kontsevich's conjecture | CONJECTURE
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 01/2018, Volume 225, pp. 242 - 283
Polynomial perturbations of real multivariate measures are discussed and corresponding Christoffel type formulas are found... 
Darboux transformations | Christoffel transformations | Bivariate product Legendre polynomials | Multivariate orthogonal polynomials | Algebraic varieties | Borel–Gauss factorization | MATHEMATICS | DETERMINANTS | Borel-Gauss factorization | LINEAR-EQUATIONS
Journal Article
Journal of number theory, ISSN 0022-314X, 2014, Volume 143, pp. 293 - 319
For any positive integer n and variables a and x we define the generalized Legendre polynomial Pn(a,x) by Pn(a,x)=∑k=0n(ak)(−1−ak)(1−x2)k... 
Generalized Legendre polynomial | Binomial coefficient | Congruence | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | SUMS
Journal Article
Tamkang Journal of Mathematics, ISSN 0049-2930, 06/2015, Volume 46, Issue 2, pp. 167 - 177
Journal Article
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