Accession Number : AD0682002

Title :   EVALUATION OF SOME DOUBLE INTEGRALS INVOLVING THE MODIFIED BESSEL FUNCTION OF ZERO ORDER.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING

Personal Author(s) : Sivazlian,B. D.

Report Date : NOV 1967

Pagination or Media Count : 19

Abstract : Let R be a region in the first quadrant of the u sub 1 - u sub 2 plane bounded by the u sub 1-axis, the u sub 2-axis and a non-increasing continuous arc Gamma, and let a sub 1 beta sub 1, beta sub 2 = 0 or 1. Integrals of the form the double integral over R of ((u sub 1 superscript alpha) e to the power ((-beta sub 1)(lambda sub 1)(u sub 1) - (beta sub 2)(lambda sub 2)(u sub 2)) I sub 0(2 the square root of ((lambda sub 1)(lambda sub 2)(u sub 1)(u sub 2)) d(u sub 1)d(u sub 2)) where I sub 0(.) is the modified Bessel function of zero order, arise in the study of a class of multi-commodity inventory systems. Explicit expressions for the integral are obtained for (alpha=0, beta sub 1=1, beta sub 2=1), (alpha=1, beta sub 1=1, beta sub 2=1), (alpha=0, beta sub 1=1, beta sub 2=0) for the two cases when R is (a) a rectangular triangle (b) a rectangle. (Author)

Descriptors :   (*INVENTORY CONTROL, MULTIPLE OPERATION), (*INTEGRALS, BESSEL FUNCTIONS), TRANSCENDENTAL FUNCTIONS, NUMERICAL INTEGRATION, GEOMETRIC FORMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE