A note on generating functions for Hausdorff moment sequences

Roth, Oliver; Ruscheweyh, Stephan; Salinas, Luís

doi:10.1090/s0002-9939-08-09460-4

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Theorem 2 (I)2

Introduction1

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2009

2021

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Cited by 3 publications

(3 citation statements)

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“…We need an estimate of ϕ(x 0 ) making explicit its dependence on a. By (26), and we have proved (20).…”

Section: Theorem 2 (I)mentioning

confidence: 93%

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Distributed order derivatives and relaxation patterns

Kochubei¹

2009

J. Phys. A: Math. Theor.

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“…We need an estimate of ϕ(x 0 ) making explicit its dependence on a. By (26), and we have proved (20).…”

Section: Theorem 2 (I)mentioning

confidence: 93%

“…(iii)-(iv) Let us prove (20). The proof of ( 21) is similar and simpler, and we leave it to the reader.…”

Section: Theorem 2 (I)mentioning

confidence: 95%

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Distributed order derivatives and relaxation patterns

Kochubei¹

2009

J. Phys. A: Math. Theor.

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On generating functions of Hausdorff moment sequences

Liu

Pego

2016

Trans. Amer. Math. Soc.

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The class of generating functions for completely monotone sequences (moments of finite positive measures on [0, 1]) has an elegant characterization as the class of Pick functions analytic and positive on (−∞, 1). We establish this and another such characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probability distribution functions on [0, 1]. Also we provide a simple analytic proof that for any real p and r with p > 0, the Fuss-Catalan or Raney numbers r pn+r pn+r n , n = 0, 1, . . . are the moments of a probability distribution on some interval [0, τ ] if and only if p ≥ 1 and p ≥ r ≥ 0. The same statement holds for the binomial coefficients pn+r−1 n , n = 0, 1, . . ..

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