Certain multidimensional integral transformations (I)

✍ Scribed by H.M. Srivastava; Rekha Panda

• Book ID: 103998149
• Publisher: Elsevier Science
• Year: 1978
• Weight: 580 KB
• Volume: 81
• Category: Article
• ISSN: 1385-7258
• DOI: 10.1016/1385-7258(78)90029-x

✦ Synopsis

The obj ect of this paper is to introduce a general multiple integral transformation whose kernel in volves the H -funct ion of several com plex variables, which was defined and studied elsewhere by the present authors ([25], [26] and [27]). This integral transform, defined by Equation (1.1) below, and its confluent form (1.15), not only provide interesting unifications (and extensions) of the various classes of known integral transformations whose kernels are ex pressible in terms of the familiar E, G and H functions of one and two variables, or the product of several such functions, but also offer the possibility of their appropriate further generalizations involving multiple integrals. Since a great variety of functions that occur rather frequently in problems of applied mathematics and mathematical analysis are special cases of the kernel used here, and since the need for a simultaneous operational calculus (based upon multidimensional integral transformations) presents it self quite naturally when problems dependent on sev eral variables are to be t reated operationally, a systematic study of the integral transform (1.1) and its confluent form (l.15) is believed to yield deeper, general and useful results.