TY - JOUR
T1 - Index integral representations for connection between cartesian, cylindrical, and spheroidal systems
AU - Passian, A.
AU - Koucheckian, S.
AU - Yakubovich, S.
PY - 2011/8
Y1 - 2011/8
N2 - 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.
AB - 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.
KW - Bessel functions
KW - Conical functions
KW - Kontorovich-lebedev and mellin transforms
KW - Mac- donald functions
KW - Spheroidal systems
UR - https://www.scopus.com/pages/publications/79960751892
U2 - 10.1080/10652469.2010.533513
DO - 10.1080/10652469.2010.533513
M3 - Article
AN - SCOPUS:79960751892
SN - 1065-2469
VL - 22
SP - 549
EP - 560
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
IS - 8
ER -