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Published January 2005 | public
Journal Article Open

The generalized Stieltjes transform and its inverse


The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter rho> 0. In previous work a convenient form of the inverse transformation was derived for the case rho= 3/2. This paper generalizes that result to all rho> 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iterated inverse Laplace transform. The form of the inverse transform derived here is a one-dimensional integral that is considerably simpler.

Additional Information

©2005 American Institute of Physics (Received 3 June 2004; accepted 16 September 2004; published online 23 December 2004) The author is grateful to Y. H. He, M. Spradlin, and A. Volovich for their collaboration in Ref. 1, which contains the r =3/2 case of the result described here. This work was supported in part by the U.S. Department of Energy under Grant No. DE-FG03-92-ER40701.


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