Accession Number : AD0017504


Title :   THE FINITE STURM-LIOUVILLE TRANSFORM


Descriptive Note : Technical rept.


Corporate Author : ILLINOIS INST OF TECH CHICAGO


Personal Author(s) : Eringen, A C


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/017504.pdf


Report Date : Aug 1953


Pagination or Media Count : 27


Abstract : Special transforms whose intervals are finite are unified and extended. A kernel is employed which may be determined to suit each particular type of problem. The Sturm-Liousville expansion is obtained for f(x) when f(x) is an integral function over (a,b) and a alxlb. The finite Sturm-Liouville transform is defined. Solutions are ontianed for some partial differential equations. Consideration is given to spherical harmonics; Hermite and Tchebycheff polynomials; and Bessel, Mathieu, and Wittaker functions. A heat conduction problem for which the solution was not known was successfully solved.


Descriptors :   *SPHERICAL HARMONICS , *INTEGRAL TRANSFORMS , FUNCTIONS , POLYNOMIALS , THERMAL CONDUCTIVITY , PARTIAL DIFFERENTIAL EQUATIONS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE