Name
Abstract | ||
|---|---|---|
The differential equation with four regular singularities located at z = 0, 1, a and ∞, called the Heun's equation (HE), is y"(z) + [/γ z ; + /δ z - 1; + /ε z - a ;] y'(z) + αβz - q / z ( z - 1) (z - a) y(z) = 0 with α + β + 1 = γ + δ + ε, and defines the Heun's operator H by H [ y ( z )] = { P 3 ( z ) D 2 + P 2 (z)D + P 1 ( Z )}[ y(z) ] with D ≡ d/d z and P i (z) polynomials of degree i . H can be factorized in the form H = [ L(z)D + M(z) ][ L(z)D + M(z) ] Polynomials L, L, M and M are given explicitly in the cases where this factorization is possible. It is shown that the value of the parameters α, β and q allowing the factorization coincides with those obtained from the F -homotopic transformation: y(z) = z ρ ( z - 1) σ ( z - a) τ y(z) forcing y(z) to be solution of a HE as y(z). |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0096-3003(02)00331-4 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Fuchsian equations,Homotopic transformations,Factorization | Differential equation,Polynomial,Mathematical analysis,Differential operator,Operator (computer programming),Factorization,Gravitational singularity,Operator theory,Mathematics | Journal |
Volume | Issue | ISSN |
141 | 1 | 0096-3003 |
Citations | PageRank | References |
6 | 1.70 | 4 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. RONVEAUX | 1 | 24 | 9.81 |