ON SOME FUNCTIONS RELATED TO THE EXPONENTIAL INTEGRALS.
Abstract
The generalized exponential integrals ((E sub n) sup m)(x) are represented in matrix form where (m) denotes the rows and n the columns. Thus, ((E sub n) sup1)(x) comprises the family of the well-known exponential integrals (E sub n)(x). Subsequent rows comprise the families of generalized exponential integrals. Associated with each row of functions are the recursion formula and derivative. When these two relations are looked upon as functional equations, they yield for each row of exponential integrals related functions much in the manner of the relationship of, say, the Legendre polynomials and Legendre functions of the second kind. This paper shows in detail the derivation of the related sets of functions and in addition the derivation of the series expressions for the first three families of exponential integrals. The purpose of these series expressions is to suggest a partiular form for the related functions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1970
- Accession Number
- AD0710217
Entities
People
- Carl Kaplan
Organizations
- Ohio State University