SPECTRAL PROPERTIES OF SOLUTIONS OF HYPERGEOMETRIC-TYPE DIFFERENTIAL-EQUATIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:50

Article

ZARZO, A ; DEHESA, JS

关键词: DIFFERENTIAL EQUATIONS;    ZEROS;    SPECIAL FUNCTIONS;    SEMICLASSICAL APPROXIMATION;   

DOI  :  10.1016/0377-0427(94)90332-8

来源: Elsevier

【 摘 要 】

The second-order differential equation sigma(X)y'' + tau(X)gamma' + lambday = 0 is usually called equation of hypergeometric type, provided that sigma, tau are polynomials of degree not higher than two and one, respectively, and lambda is a constant. Their solutions are commonly known as hypergeometric-type functions (HTFs). In this work, a study of the spectrum of zeros of those HTFs for which lambda = -nutau' - 1/2nu(nu - 1)sigma'', nu is-an-element-of R, and sigma, tau are independent of nu, is done within the so-called semiclassical (or WKB) approximation. Specifically, the semiclassical or WKB density of zeros of the HTFs is obtained analytically in a closed way in terms of the coefficients of the differential equation that they satisfy. Applications to the Gaussian and confluent hypergeometric functions as well as to Hermite functions are shown.

【 授权许可】

Free