Discrete index Whittaker transforms

2020/09/25 by Yakubovich, Semyon
#33C10 #33C15 #42A16 #44A15 #45A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.12238

Abstract

Discrete analogs of the index Whittaker transform are introduced and investigated. It involves series and integrals with respect to a second parameter of the Whittaker function W_μ, i n (x), x >0, μ∈ ℝ, n ∈ ℕ, i is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established.

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