Accession Number : AD0425594

Title :   MODIFIED HANKEL FUNCTIONS AND THEIR INTEGRALS TO ARGUMENT 10,

Corporate Author : PENNSYLVANIA STATE UNIV UNIVERSITY PARK ORDNANCE RESEARCH LAB

Personal Author(s) : Singh,K. ; Lumley,J. L. ; Betchov,R.

Report Date : OCT 1963

Pagination or Media Count : 29

Abstract : For analyses of the stability of laminar flows, solutions of Stokes' equation are used to construct asymptotic solutions of the Orr-Sommerfeld equation. The pertinent solutions are the second integrals of the modified Hankel functions of order one-third. Tables of these functions and their derivatives for arguments bounded in absolute value by 6 were published by the Harvard Computation Laboratory in 1945; no tables of the integrals existed. In 1959 R. Betchov, starting from the Harvard tables, computed the first two integrals for use in a study of boundary layer oscillation, but his computations were not published. Kirtan Singh has extended the Harvard values of the modified Hankel functions to an argument of =10 (on the imaginary axis), recomputing the values beyond 5.0, and has determined the first and second integrals in the same range. These new values, together with Betchov's integrals to an argument of =5, are published here for the first time. The values of the functions themselves to an argument of =5 are reproduced by permission of the Harvard Computation Laboratory. (Author)

Descriptors :   (*LAMINAR BOUNDARY LAYER, STABILITY), (*SPECIAL FUNCTIONS (MATHEMATICAL), TABLES(DATA)), INTEGRALS, SERIES(MATHEMATICS), OSCILLATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE