Accession Number : AD0710217

Title :   ON SOME FUNCTIONS RELATED TO THE EXPONENTIAL INTEGRALS.

Descriptive Note : Final rept.,

Corporate Author : OHIO STATE UNIV RESEARCH FOUNDATION COLUMBUS

Personal Author(s) : Kaplan,Carl

Report Date : JUN 1970

Pagination or Media Count : 23

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)

Descriptors :   (*INTEGRALS, SPECIAL FUNCTIONS(MATHEMATICAL)), EXPONENTIAL FUNCTIONS, NAVIER STOKES EQUATIONS, MATRICES(MATHEMATICS), THERMAL RADIATION, NUMERICAL INTEGRATION, SERIES(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE