Tables of Mellin Transforms

Oberhettinger, Fritz

doi:10.1007/978-3-642-65975-1

Cited by 299 publications

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“…In fact, ∞ 0 f X (x)dx = 1, from formula 13.39 in Oberhettinger (1974) and binomial expansion of (1 + x) α for |x| < 1. (b) From the density for the sum of two random variables in Rohatgi (1976),…”

Section: Property Of a Bivariate Density Based On The General Exponenmentioning

confidence: 99%

Reliability estimation and ratio distribution in a general exponential distribution

Lee¹,

Moon²

2014

Journal of the Korean Data and Information Science Society

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We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P (X < Y ) and the skewness trends of the density function of the ratio X/(X + Y ) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.

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Section: Property Of a Bivariate Density Based On The General Exponenmentioning

confidence: 99%

Reliability estimation and ratio distribution in a general exponential distribution

Lee¹,

Moon²

2014

Journal of the Korean Data and Information Science Society

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“…From the density (3.1) and formula 2.29 in Oberhettinger (1974), k-th moment of the ratio R is obtained as follows.…”

Section: Distribution Of Ratio Y /(X + Y )mentioning

confidence: 99%

Some properties of reliability, ratio, maximum and minimum in a bivariate exponential distribution with a dependence parameter

Lee¹,

Kang²

2014

Journal of the Korean Data and Information Science Society

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“…For more information regarding the Mellin integral transform including its properties and particular cases we refer the interested reader to e.g. [2], [3], [5], [15], [20], [28], [30], [32], and [35].…”

Section: Basic Definitions and Properties Of The Mellin Transformmentioning

confidence: 99%

“…in [5], [28], [30], and [32]. We specify here the Mellin transform formulas that are used in the further discussions, namely:…”

Section: Basic Definitions and Properties Of The Mellin Transformmentioning

confidence: 99%

The mellin integral transform in fractional calculus

Luchko

Kiryakova

2013

fcaa

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In Fractional Calculus (FC), the Laplace and the Fourier integral transforms are traditionally employed for solving different problems. In this paper, we demonstrate the role of the Mellin integral transform in FC. We note that the Laplace integral transform, the sin-and cos-Fourier transforms, and the FC operators can all be represented as Mellin convolution type integral transforms. Moreover, the special functions of FC are all particular cases of the Fox H-function that is defined as an inverse Mellin transform of a quotient of some products of the Gamma functions.In this paper, several known and some new applications of the Mellin integral transform to different problems in FC are exemplarily presented. The Mellin integral transform is employed to derive the inversion formulas for the FC operators and to evaluate some FC related integrals and in particular, the Laplace transforms and the sin-and cos-Fourier transforms of some special functions of FC. We show how to use the Mellin integral transform to prove the Post-Widder formula (and to obtain its new modification), to derive some new Leibniz type rules for the FC operators, and to get new completely monotone functions from the known ones.

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Tables of Mellin Transforms

Cited by 299 publications

References 0 publications

Reliability estimation and ratio distribution in a general exponential distribution

Reliability estimation and ratio distribution in a general exponential distribution

Some properties of reliability, ratio, maximum and minimum in a bivariate exponential distribution with a dependence parameter

The mellin integral transform in fractional calculus

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