Name
Abstract | ||
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Given a polynomial solution of a differential equation, its m -ary decomposition, i.e. its decomposition as a sum of m polynomials P [ j ] ( x ) = ∑ k α j , k x λ j , k containing only exponents λ j , k with λ j , k + 1 − λ j , k = m , is considered. A general algorithm is proposed in order to build holonomic equations for the m -ary parts P [ j ] ( x ) starting from the initial one, which, in addition, provides a factorized form of them. Moreover, these differential equations are used to compute expansions of the m -ary parts of a given polynomial in terms of classical orthogonal polynomials. As illustration, binary and ternary decomposition of these classical families are worked out in detail. References References 1 I. Area E. Godoy A. Ronveaux A. Zarzo Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: discrete case J. Comput. Appl. Math. 89 1998 309 325 2 I. Area, E. Godoy, A. Ronveaux, A. Zarzo, q , m 3 E. Beke Die irreducibilität der homogenen linearen differentialgleichungen Math. Ann. 45 1894 278 294 4 E. Beke Die symmetrischen functionen bei linearen homogenen differentialgleichungen Math. Ann. 45 1894 295 300 5 Y. Ben Cheikh A generalization of even and odd functions 1991 6 T.S. Chihara An Introduction to Orthogonal Polynomials 1978 Gordon and Breach New York 7 E. Godoy A. Ronveaux A. Zarzo I. Area Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: continuous case J. Comput. Appl. Math. 84 1997 257 275 8 E. Hendriksen H. van Rossum Semi-classical orthogonal polynomials C.et al. Brenzinski Polynômes Orthogomant et Applications 1985 Springer Berlin 354 361 9 M.E.H. Ismail On sieved orthogonal polynomials IV: generating functions J. Approx. Theory 46 1986 284 296 10 W. Koepf 11 F. Marcellán G. Sansigre Quadratic decomposition of orthogonal polynomials: a matrix approach Numer. Algorithms 3 1992 285 298 12 P. Maroni Prolégomene a l’etude des polynômes orthogonaux semi-classiques orthogonaux (I) Ann. Math. Pure Appl. 149 1987 165 184 13 P. Maroni Sur la décomposition quadratique d’une suite de polynômes orthogonaux (I) Rivista di Mat. Pura ed Appl. 6 1990 19 53 14 A.F. Nikiforov S.K. Suslov V.B. Uvarov Classical Orthogonal Polynomials of a Discrete Variable 1991 Springer Berlin 15 A. Ronveaux, S. Belmehdi, E. Godoy, A. Zarzo, 1996, 319, 335 16 A. Ronveaux A. Zarzo E. Godoy Recurrence relation for connection coefficients between two families of orthogonal polynomials J. Comput. Appl. Math. 62 1995 67 73 17 B. Salvy P. Zimmermann GFUN: a Maple package for the manipulation of generating and holonomic functions of one variable ACM Trans. Math. Softw. 20 1994 163 177 18 R.P. Stanley Differentiably finite power series Eur. J. Comb. 1 1980 175 188 19 S. Wolfram The Mathematica Book 1996 Wolfram Media/Cambridge University Press Champaign 20 A. Zarzo I. Area E. Godoy A. Ronveaux Results for some inversion problems for classical continuous and discrete orthogonal polynomials J. Phys. A: Math. Gen. 30 1997 L35 L40 |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1006/jsco.1999.0337 | Journal of Symbolic Computation |
Keywords | DocType | Volume |
cyclic group,order m | Journal | 28 |
Issue | ISSN | Citations |
6 | Journal of Symbolic Computation | 0 |
PageRank | References | Authors |
0.34 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. RONVEAUX | 1 | 24 | 9.81 |
| A. Zarzo | 2 | 2 | 1.48 |
| I. Area | 3 | 4 | 3.35 |
| Eduardo Godoy | 4 | 18 | 6.92 |