Results 21 to 30 of about 206 (77)
The geometric mean is a Bernstein function [PDF]
, 2013 In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of $n$ positive numbers.
Li, Wen-Hui, Qi, Feng, Zhang, Xiao-Jing
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Abelian theorems for Whittaker transforms
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 3, Page 417-431, 1987., 1986 Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
Richard D. Carmichael, R. S. Pathak
wiley +1 more source
Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators [PDF]
, 2015 For each of the eight $n$-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given.
Koornwinder, Tom H.
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Recent developments on the Stieltjes transform of generalized functions
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 4, Page 641-670, 1987., 1986 This paper is concerned with recent developments on the Stieltjes transform of generalized functions. Sections 1 and 2 give a very brief introduction to the subject and the Stieltjes transform of ordinary functions with an emphasis to the inversion theorems.
Ram Sankar Pathak, Lokenath Debnath
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Theta and Riemann xi function representations from harmonic oscillator eigensolutions
, 2006 From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A
Abramowitz +25 more
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Supercongruences and Complex Multiplication [PDF]
, 2012 We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers.
Kibelbek, Jonas +4 more
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Analytic representation of the distributional finite Hankel transform
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 2, Page 325-344, 1985., 1985 Various representations of finite Hankel transforms of generalized functions are obtained. One of the representations is shown to be the limit of a certain family of regular generalized functions and this limit is interpreted as a process of truncation for the generalized functions (distributions). An inversion theorem for the gereralized finite Hankel
O. P. Singh, Ram S. Pathak
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A generalized Meijer transformation
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 2, Page 359-365, 1985., 1985 In a series of papers [1‐6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function (st) νη(q, ν + 1; (st)q). This transformation is referred to as GM transformation which reduces to the classical Meijer transform when q = 1.
G. L. N. Rao, L. Debnath
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A representation of Jacobi functions
International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 4, Page 707-717, 1985., 1985 Recently, the continuous Jacobi transform and its inverse are defined and studied in [1] and [2]. In the present work, the transform is used to derive a series representation for the Jacobi functions , −½ ≤ α, β ≤ ½, α + β = 0, and λ ≥ −½. The case α = β = 0 yields a representation for the Legendre functions and has been dealt with in [3].
E. Y. Deeba, E. L. Koh
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The continuous Jacobi transform
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 1, Page 145-160, 1983., 1982 The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into where w(x) = (1 − x) α(1 + x) β.
E. Y. Deeba, E. L. Koh
wiley +1 more source