6533b7d2fe1ef96bd125f426
RESEARCH PRODUCT
New special function recurrences giving new indefinite integrals
John T. Conwaysubject
Pure mathematicsRecurrence relationDifferential equationApplied Mathematics010102 general mathematics010103 numerical & computational mathematicsParabolic cylinder functionFunction (mathematics)01 natural sciencesLegendre functionIntegrating factorsymbols.namesakeSpecial functionssymbols0101 mathematicsAnalysisBessel functionMathematicsdescription
ABSTRACTSequences of new recurrence relations are presented for Bessel functions, parabolic cylinder functions and associated Legendre functions. The sequences correspond to values of an integer variable r and are generalizations of each conventional recurrence relation, which correspond to r=1. The sequences can be extended indefinitely, though the relations become progressively more intricate as r increases. These relations all have the form of a first-order linear inhomogeneous differential equation, which can be solved by an integrating factor. This gives a very general indefinite integral for each recurrence. The method can be applied to other special functions which have conventional recurrence relations. All results have been checked numerically using Mathematica.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-07-20 | Integral Transforms and Special Functions |