On The Degenerate Laplace Transform-I

Upadhyaya, Lalit Mohan

doi:10.5958/2320-3226.2018.00001.2

Cited by 6 publications

(6 citation statements)

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“…We now have the following definition: Definition 1. [3,[8][9][10][11][12][13][14] For any nonzero real number λ, the degenerate exponential function is defined as follows:…”

Section: Definition and Some Explicit Formulasmentioning

confidence: 99%

“…Pioneering work of T. Kim and D. S. Kim [8] introduced the concept of degenerate gamma functions and degenerate Laplace transforms, as well as the derivation of fundamental properties. Subsequently, L. M. Upadhyaya [14][15][16] further delved into properties of the degenerate Laplace transform, while U. Duran [4] investigated the degenerate Sumudu transform and L. M. Upadhyaya et.al [1] defined the degenerate Elzaki transform and its properties.…”

Section: Introductionmentioning

confidence: 99%

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On Degenerate Laplace-type Integral Transform

Campos,

Fernandez,

Natuil

2023

Eur. J. Pure Appl. Math.

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This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms.

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“…We now have the following definition: Definition 1. [3,[8][9][10][11][12][13][14] For any nonzero real number λ, the degenerate exponential function is defined as follows:…”

Section: Definition and Some Explicit Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Degenerate Laplace-type Integral Transform

Campos,

Fernandez,

Natuil

2023

Eur. J. Pure Appl. Math.

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“…The sequence of polynomials {S n (x)} is called the Sheffer sequence for (g(t), f (t)) and is denoted by S n (x) ∼ (g(t), f (t)). It is known [7] (Theorem 3.5.5) that the set of Sheffer sequences is a group of umbral composition: The identity under umbral composition is x n ∼ (1, t) and the inverse of the sequence S n (x) ∼ (g(t), f (t)) is the Sheffer sequence for ( of polynomials which can be asymptotically extended to some special generating functions such as transcendental functions [19,27].…”

Section: Introductionmentioning

confidence: 99%

A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types

Kim

2019

Mathematics

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We study some properties of Sheffer sequences for some special polynomials with complex Changhee and Daehee polynomials introducing their complex versions of the polynomials and splitting them into real and imaginary parts using trigonometric polynomial sequences. Moreover, considering their degenerate types of Sheffer sequences based on umbral composition, we present some useful expressions, properties, and examples about complex versions of the degenerate polynomials.

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“…(1 + λt) − 1 λ t s−1 dt, (see [9]) (1.4) and degenerate Laplace transformation which was defined by (1 + λt) − s λ f (t)dt, (see [9,15]) (1.5) if the integral converges. The authors obtained some properties and interesting formulas related to the degenerate gamma function.…”

Section: Introductionmentioning

confidence: 99%