Results 1 to 10 of about 542 (54)
Pochhammer symbol with negative indices. A new rule for the method of brackets
Open Mathematics, 2016 The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.
Gonzalez Ivan, Jiu Lin, Moll Victor H
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Bulletin of the London Mathematical Society, Volume 53, Issue 1, Page 285-299, February 2021., 2021 Abstract The expected signature is an analogue of the Laplace transform for probability measures on rough paths. A key question in the area has been to identify a general condition to ensure that the expected signature uniquely determines the measures.
Horatio Boedihardjo +3 more
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Integral transforms involving a generalized k-Bessel function
Demonstratio Mathematica, 2023 The main goal of this study was to look into some new integral transformations that are associated with a generalized kk-Bessel function. Integral formulas for the generalized kk-Bessel function have been established using the Laplace transform, Euler ...
Khammash Ghazi S. +4 more
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Partial sums of the Rabotnov function
Acta Universitatis Sapientiae: Mathematica, 2022 This article deals with the ratio of normalized Rabotnov function ℝα,β (z) and its sequence of partial sums (ℝα,β)m (z). Several examples which illustrate the validity of our results are also given.
Kazımoğlu Sercan, Deniz Erhan
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On some geometric results for generalized k-Bessel functions
Demonstratio Mathematica, 2023 The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized kk-Bessel functions, such as the radii of uniform convexity and of α\alpha -convexity.
Toklu Evrim
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Turán-Type Inequalities for Bessel, Modified Bessel and Kr ̈tzel Functions
Journal of Kufa for Mathematics and Computer, 2018 We establish Turán-type inequalities for Bessel functions, modified Bessel functions, Kr ̈tzel function and Beta function, by using a new form of Cauchy–Bunyakovsky–Schwarz inequality.
Piyush Kumar Bhandari, S. K. Bissu
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Interlacing of positive real zeros of Bessel functions [PDF]
, 2010 We unify the three distinct inequality sequences (Abramowitz ans Stegun (1972) [1,9.5.2]) of positive real zeros of Bessel functions into a single one.Comment: 4 ...
Abramowitz +5 more
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An extension of the method of brackets. Part 2
Open Mathematics, 2020 The method of brackets, developed in the context of evaluation of integrals coming from Feynman diagrams, is a procedure to evaluate definite integrals over the half-line. This method consists of a small number of operational rules devoted to convert the
Gonzalez Ivan, Jiu Lin, Moll Victor H.
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Comment on the orthogonality of the Macdonald functions of imaginary order [PDF]
, 2009 Recently, Yakubovich [Opuscula Math. 26 (2006) 161--172] and Passian et al. [J. Math. Anal. Appl. doi:10.1016/j.jmaa.2009.06.067] have presented alternative proofs of an orthogonality relation obeyed by the Macdonald functions of imaginary order. In this
Bielski, Sebastian +1 more
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On the Lebedev transformation in Hardy′s spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 66, Page 3603-3616, 2004., 2004 We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy′s space H2,A, A > 0. This gives another version of the Fourier‐integral‐type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space H⌢2,A≡H⌢2((−A,A);|Γ(1+Rez+iτ)|2dτ),
Semyon B. Yakubovich
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