On the Fractional Sums of Some Special Functions
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DOI: 10.1007/s00025-019-0964-4
Abstract: We obtain new relations involving the Lerch transcendent and establish some closed-form expressions using special functions like the Riemann and Hurwitz zeta functions and fractional sums. We also get some formulae for the specific values… read more here.
Keywords: functions fractional; special functions; fractional sums; sums special ... See more keywords
Evaluation of integral transforms using special functions with applications to biological tissues
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DOI: 10.1007/s40314-021-01542-2
Abstract: In this paper, we aim to establish several new closed-form evaluations of certain integral transforms involving the rational and exponential functions, which are expressed in terms of confluent hypergeometric function and related functions. Also, we… read more here.
Keywords: special functions; integral transforms; evaluation integral; biological tissues ... See more keywords
Integrals of Special Functions and Umbral Methods
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DOI: 10.1007/s40819-021-01047-w
Abstract: We derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of… read more here.
Keywords: special functions; functions umbral; umbral methods; integrals special ... See more keywords
Representation and evaluation of the Arrhenius and general temperature integrals by special functions
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DOI: 10.1016/j.tca.2021.179034
Abstract: Abstract The non-isothermal analysis of reactions with a constant heating rate involves a temperature integral. This integral is popularized as the Arrhenius integral, but when the pre-exponential factor of the Arrhenius equation depends on temperature… read more here.
Keywords: general temperature; activation energy; special functions; power law ... See more keywords
Groups, Jacobi functions, and rigged Hilbert spaces
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DOI: 10.1063/1.5138238
Abstract: This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations… read more here.
Keywords: harmonics; special functions; groups jacobi; rigged hilbert ... See more keywords
Indefinite integrals of special functions from integrating factors
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DOI: 10.1080/10652469.2019.1689567
Abstract: ABSTRACT Some general integrals are presented which were obtained from two integrating factors and for the first two and last two terms, respectively, of the second-order linear ordinary differential equation obeyed by many special functions.… read more here.
Keywords: integrating factors; functions integrating; indefinite integrals; integral transforms ... See more keywords
Infinite series involving special functions obtained using simple one-dimensional quantum mechanical problems
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/adbd9b
Abstract: In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an infinite… read more here.
Keywords: special functions; quantum mechanical; series; infinite sums ... See more keywords
Techniques for Obtaining Non-Divergent Series as Alternatives to Divergent Asymptotic Series for Special Functions and Integrals
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DOI: 10.1109/tap.2025.3569379
Abstract: This work discusses approximate evaluations of some types of integrals arising in electromagnetic problems. An integral can be transformed into a divergent asymptotic series by replacing the function within the integral with a power series… read more here.
Keywords: asymptotic series; special functions; series; non divergent ... See more keywords
Radii of γ-Spirallike of q-Special Functions
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DOI: 10.3390/math12142261
Abstract: The geometric properties of q-Bessel and q-Bessel-Struve functions are examined in this study. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit… read more here.
Keywords: special functions; radii spirallike; spirallike special; bessel struve ... See more keywords
Inequalities for Basic Special Functions Using Hölder Inequality
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DOI: 10.3390/math12193037
Abstract: Let p,q≥1 be two real numbers such that 1p+1q=1, and let a,b∈R be two parameters defined on the domain of a function, for example, f. Based on the well known Hölder inequality, we propose a… read more here.
Keywords: basic special; special functions; inequalities basic; inequality ... See more keywords
Unified Approach to Fractional Calculus Images of Special Functions—A Survey
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DOI: 10.3390/math8122260
Abstract: Evaluation of images of special functions under operators of fractional calculus has become a hot topic with hundreds of recently published papers. These are growing daily and we are able to comment here only on… read more here.
Keywords: special functions; images special; fractional calculus; unified approach ... See more keywords