Generalized Stieltjes transforms: basic aspects

2011/11/18 by Dmitry Karp, Karp, Dmitry, Elena Prilepkina +1
Mathematics · #26A33 #26A48 #44A15 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:26A33 #msc:26A48 #msc:44A15

paper · pdf · doi:10.48550/arxiv.1111.4271

23 pages, no figures; a counterexample related to complex variable chracterization added; some typos corrected, other minore improvements made

arxiv created 2012/02/11 · arxiv updated 2012/02/14

Abstract

The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical examples. The paper includes an appendix, where we define the left sided Riemann-Liouville and the right sided Kober-Erdelyi fractional integrals of measures supported on half axis and give inversion formulas for them.

Related

• Hypergeometric functions as generalized Stieltjes transforms
• To the theory of generalized Stieltjes transforms
• Some integrals and series involving the Stieltjes constants
• Computing Inverses of Stieltjes Transforms of Probability Measures
• Evaluation of multivariate integrals based on a duality identity for the\n Stieltjes transform