A holonomic systems approach to special functions identities

TY - JOUR

T1 - A holonomic systems approach to special functions identities

AU - Zeilberger, Doron

N1 - Funding Information: * Supported in part by NSF grant DMS 8800663.

PY - 1990/12/10

Y1 - 1990/12/10

N2 - We observe that many special functions are solutions of so-called holonomic systems. Bernstein's deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps. This is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE.

AB - We observe that many special functions are solutions of so-called holonomic systems. Bernstein's deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps. This is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE.

KW - Elimination

KW - Weyl algebra

KW - computer algebra

KW - hypergeometric series

KW - partial difference operators

UR - http://www.scopus.com/inward/record.url?scp=0001601404&partnerID=8YFLogxK

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U2 - https://doi.org/10.1016/0377-0427(90)90042-X

DO - https://doi.org/10.1016/0377-0427(90)90042-X

M3 - Article

VL - 32

SP - 321

EP - 368

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 3

ER -