Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]
Notes on Number Theory and Discrete MathematicsWe consider a polylogarithm expression containing complex arguments, namely šĀ±(n)=ā(Liā((1Ā±i)/2)). The central notion of the present paper is to evaluate the real parts of šĀ±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
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The density structure and star formation rate of non-isothermal polytropic turbulence [PDF]
, 2015 The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF).
Banerjee, Supratik, Federrath, Christoph
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On approximating the modified Bessel function of the second kind
Journal of Inequalities and Applications, 2017 In the article, we prove that the double inequalities Ļ e ā x 2 ( x + a ) < K 0 ( x ) < Ļ e ā x 2 ( x + b ) , 1 + 1 2 ( x + a ) < K 1 ( x ) K 0 ( x ) < 1 + 1 2 ( x + b ) $$ \frac{\sqrt{\pi}e^{-x}}{\sqrt{2(x+a)}}< K_{0}(x)< \frac{\sqrt{\pi }e^{-x}}{\sqrt ...
Zhen-Hang Yang, Yu-Ming Chu
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On the Nonlinear Integro-Differential Equations
Fractal and Fractional, 2021 The goal of this paper is to study the uniqueness of solutions of several nonlinear LiouvilleāCaputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces.
Chenkuan Li, Joshua Beaudin
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A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions
Axioms, 2019 The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions.
Maxie D. Schmidt
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Completely monotonic functions involving the gamma and $q$-gamma functions [PDF]
Proceedings of the American Mathematical Society, 2005 The authors provide new examples of logarithmically completely monotonic functions. These examples are ratios of products involving the Gamma function or the \(q\)-Gamma function. As an application of these results new examples of infinitely divisible probability distributions can be obtained.
Grinshpan, Arcadii Z. +1 more
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Generalized Extended Matrix Variate Beta and Gamma Functions and Their Applications
IngenierĆa y Ciencia, 2016 In this article, we define and study generalized forms of extended matrix variate gamma and beta functions. By using a number of results from matrix algebra, special functions of matrix arguments and zonal polynomials we derive a number of properties of ...
Daya K. Nagar +2 more
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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
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Some Results of Extended Beta Function and Hypergeometric Functions by Using Wimanās Function
Mathematics, 2021 The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function.
Shilpi Jain +4 more
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