On Generalized Exponential Integrals and Related Functions.
Abstract
The so called 'exponential' function Y(Sup m)(Sub n) (x) is governed by an (m+1)nth order homogeneous differential equation and includes the generalized exponential integrals E(sup m)(sub n) (x) and their related functions F(sup m)(sub n) (x). In the present paper, recursion formulas and differential relations similar to those for the generalized exponential integrals are imposed on the Y(Sup m)(sub n) (x). As a result, the multiplicity of arbitrary constants independent of n. Furthermore, the form of the related functions is such that it suggests comparison with the series expansions of the generalized exponential integrals. This comparison leads to expressions for the arbitrary constants in terms of Riemann Zeta functions involving only even values of the argument. Finally, the series expansion for the generalized exponential integral of order (m) is shown to be equal to the related function of order (m+1) plus a rapidly convergent power series in the independent variable x. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1971
- Accession Number
- AD0734541
Entities
People
- Carl Kaplan
Organizations
- Johns Hopkins University