About the Project
NIST

accessory parameter

AdvancedHelp

(0.001 seconds)

8 matching pages

1: 31.13 Asymptotic Approximations
§31.13 Asymptotic Approximations
For asymptotic approximations for the accessory parameter eigenvalues q m , see Fedoryuk (1991) and Slavyanov (1996). …
2: 31.18 Methods of Computation
The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 2830.
3: 31.4 Solutions Analytic at Two Singularities: Heun Functions
For an infinite set of discrete values q m , m = 0 , 1 , 2 , , of the accessory parameter q , the function H ( a , q ; α , β , γ , δ ; z ) is analytic at z = 1 , and hence also throughout the disk | z | < a . … The eigenvalues q m satisfy the continued-fraction equation …
4: 31.14 General Fuchsian Equation
The three sets of parameters comprise the singularity parameters a j , the exponent parameters α , β , γ j , and the N - 2 free accessory parameters q j . …
5: 31.2 Differential Equations
All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, { } , can be transformed into (31.2.1). The parameters play different roles: a is the singularity parameter; α , β , γ , δ , ϵ are exponent parameters; q is the accessory parameter. …
6: 31.16 Mathematical Applications
It describes the monodromy group of Heun’s equation for specific values of the accessory parameter. …
7: 31.15 Stieltjes Polynomials
In this case the accessory parameters q j are given by …
8: 31.11 Expansions in Series of Hypergeometric Functions
In this case the accessory parameter q is a root of the continued-fraction equation …