E-transforms (II)
F. M. Ragab · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · 1967
The following class of inte gral transform pairs is established(2)The kernel in the tra nsform (1) is Mac Robert's E•func tion and integration is performed with res pect to the arg ume nt of thi s fun ction.In the inversion formula (2), the kernel is like wise a n E-fun ction, but the integration is performed with respect to its parameters.Known spec ial cases of thi s ge neral transform pair is the Kantorovich-Lebedev transform s pair:r tKixfy)ffy)dy , 7r 0 fIx) = f o oo Ki y(X)g(y)dy , and the ge neralized Mehler trans form pair g(x) = -;sinh (7rx)r(!-k+ iX)r(!-k -iX) 1. 00 pkix _t/2 fy)ffy)dy , fIx) = 10 00 P~y-t/2 (x)g(y) dy.