Index integral representations for connection between cartesian, cylindrical, and spheroidal systems

Journal Article · Sat Jan 01 00:00:00 EST 2011 · Integral Transforms and Special Functions

DOI:https://doi.org/10.1080/10652469.2010.533513· OSTI ID:1022024

Passian, Ali ^[1]; Koucheckian, Sherwin ^[2]; Yakubovich, Semyon ^[3]

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1. ORNL
2. University of South Florida, Tampa
3. University of Porto, Portugal

In this paper, we present two new index integral representations for connection between cartesian, cylindrical, and spheroidal coordinate systems in terms of Bessel, MacDonald, and conical functions. Our result is mainly motivated by solution of the boundary value problems in domains composed of both cartesian and hyperboloidal boundaries, and the need for new integral representations that facilitate the transformation between these coordinates. As a by-product, the special cases of our results will produce new proofs to known index integrals and provide some new integral identities.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1022024
• Journal Information: Integral Transforms and Special Functions, Vol. 22, Issue 8; ISSN 1065--2469
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BESSEL FUNCTIONS
BOUNDARY-VALUE PROBLEMS
COORDINATES
INTEGRALS
TRANSFORMATIONS