Some identities for the Glasser transform and their applications

In the present paper we consider a new integral transform, denoted by $\mathcal{G}_{\nu}$, which may be regarded as a generalization of the well-known transform due to Glasser. Many identities involving this transform are given. By making use of these identities, a number of new Parseval--Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustrations of the results presented here.

Anahtar Kelimeler:

Laplace transforms, Widder potential transforms, Fourier sine transforms, Fourier cosine transforms, $\mathcal{H} _{\nu}$-transforms, $\mathcal{K}_{\nu}$-transforms, Parseval--Goldstein type theorems

Some identities for the Glasser transform and their applications

Keywords:

Laplace transforms, Widder potential transforms, Fourier sine transforms, Fourier cosine transforms, $\mathcal{H} _{\nu}$-transforms, $\mathcal{K}_{\nu}$-transforms, Parseval--Goldstein type theorems,

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Dernek A, Dernek N, Yürekli O. Identities for the Hankel transform and their applications. J Math Anal Appl 2009; 354: 165—176.
Erdélyi A, Magnus W, Oberhettinger F, Tricomi FG. Tables of Integral Transforms. Vol. 1, New York, NY, USA: McGraw—Hill, 1954.
Erdélyi A, Magnus W, Oberhettinger F, Tricomi FG. Tables of Integral Transforms. Vol. 2, New York, NY, USA: McGraw—Hill, 1954.
Glasser ML. Some Bessel function integrals. Kyungpook Math J 1973; 13: 171—174.
Gradshteyn IS, Ryzhik IM. Table of Integrals, Series and Products, 6th edition, New York, NY, USA: Academic Press, 2000.
Kahramaner Y, Srivastava HM, Yürekli 0. A theorem on the Glasser transform and its applications. Complex
Variables Theory Appl 1995; 27: 7—15.
Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and Series, Vol. 2, Special Functions, New York, NY, USA:
Gordon and Breach, 1986.
Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and Series, Vol. 4, Direct Laplace Transforms, New York, NY,
USA: Gordon and Breach, 1990.
Srivastava HM, Yiirekli O. A theorem on a Stieltjes-type integral transform and its applications. Complex Variables
Theory Appl 1995; 28: 159—168.