The Fox–Wright functions and Laguerre multiplier sequences

Craven, Thomas C.; Csordás, George

doi:10.1016/j.jmaa.2005.03.058

Cited by 56 publications

(18 citation statements)

References 20 publications

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“…Several articles have been devoted to this problem (see [Dzh84,DzhNer68,OstPer97,Poly21,Pop02,Psk05,Sed94,Sed00,Wim05b]). Also studied is the related question of the distribution of zeros of sections and tails of the Mittag-Leffler function (see [Ost01,Zhe02]) and of some associated special functions (see [GraCso06,Luc00]). Also studied is the related question of the distribution of zeros of sections and tails of the Mittag-Leffler function (see [Ost01,Zhe02]) and of some associated special functions (see [GraCso06,Luc00]).…”

Section: Historical and Bibliographical Notesmentioning

confidence: 99%

Mittag-Leffler Functions, Related Topics and Applications

Gorenflo¹,

Kilbas²,

Mainardi³

et al. 2014

Springer Monographs in Mathematics

1,068

871

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Section: Historical and Bibliographical Notesmentioning

confidence: 99%

Mittag-Leffler Functions, Related Topics and Applications

Gorenflo¹,

Kilbas²,

Mainardi³

et al. 2014

Springer Monographs in Mathematics

1,068

871

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“…= (x + 1) a is real-rooted. Furthermore, by [7,Theorem 3.14], also { 2i i 1 i! } i≥0 is a multiplier sequence.…”

Section: 5mentioning

confidence: 99%

Arithmetic Aspects of Symmetric Edge Polytopes

2019

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We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Gröbner basis techniques, half-open decompositions and methods for interlacings polynomials we provide an explicit formula for the h * -polynomial in case of complete bipartite graphs. In particular, we show that the h * -polynomial is γ-positive and real-rooted. This proves Gal's conjecture for arbitrary flag unimodular triangulations in this case, and, beyond that, we prove a strengthing due to Nevo and Petersen (2011).2010 Mathematics Subject Classification. 05A15, 52B12 (primary); 13P10, 26C10, 52B15, 52B20 (secondary).

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“…Moreover, if for the function ϕ ∈ LPI we have γ k ≥ 0 for all k ∈ N 0 , we say that ϕ ∈ LP + . Further information about the Laguerre-Pólya class can be found in [CC06], [Ob63] and [DC09].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Zeros of some special entire functions

Baricz

Singh

2018

Proc. Amer. Math. Soc.

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Abstract. The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, Pólya and Runckel. The obtained results extend the known theorem of Hurwitz on exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and cross-product of Bessel functions are also given, which are related to some recent open problems.

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The Fox–Wright functions and Laguerre multiplier sequences

Cited by 56 publications

References 20 publications

Mittag-Leffler Functions, Related Topics and Applications

Mittag-Leffler Functions, Related Topics and Applications

Arithmetic Aspects of Symmetric Edge Polytopes

Zeros of some special entire functions

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