About the Project
NIST

polynomial solutions

AdvancedHelp

(0.003 seconds)

1—10 of 66 matching pages

1: 29.17 Other Solutions
If (29.2.1) admits a Lamé polynomial solution E , then a second linearly independent solution F is given by …
2: 18.40 Methods of Computation
3: 31.15 Stieltjes Polynomials
§31.15(i) Definitions
Stieltjes polynomials are polynomial solutions of the Fuchsian equation (31.14.1). …There exist at most ( n + N - 2 N - 2 ) polynomials V ( z ) of degree not exceeding N - 2 such that for Φ ( z ) = V ( z ) , (31.15.1) has a polynomial solution w = S ( z ) of degree n . … If z 1 , z 2 , , z n are the zeros of an n th degree Stieltjes polynomial S ( z ) , then every zero z k is either one of the parameters a j or a solution of the system of equations … If t k is a zero of the Van Vleck polynomial V ( z ) , corresponding to an n th degree Stieltjes polynomial S ( z ) , and z 1 , z 2 , , z n - 1 are the zeros of S ( z ) (the derivative of S ( z ) ), then t k is either a zero of S ( z ) or a solution of the equation …
4: 18.38 Mathematical Applications
Differential Equations
5: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
is a polynomial of degree n , and hence a solution of (31.2.1) that is analytic at all three finite singularities 0 , 1 , a . These solutions are the Heun polynomials. …
6: 18.39 Physical Applications
§18.39(i) Quantum Mechanics
The corresponding eigenfunctions are … A second example is provided by the three-dimensional time-independent Schrödinger equation …
7: 28.31 Equations of Whittaker–Hill and Ince
§28.31(ii) Equation of Ince; Ince Polynomials
When p is a nonnegative integer, the parameter η can be chosen so that solutions of (28.31.3) are trigonometric polynomials, called Ince polynomials. …
8: 31.1 Special Notation
Sometimes the parameters are suppressed.
9: Bibliography S
  • R. Shail (1978) Lamé polynomial solutions to some elliptic crack and punch problems. Internat. J. Engrg. Sci. 16 (8), pp. 551–563.
  • 10: 32.10 Special Function Solutions
    §32.10(iv) Fourth Painlevé Equation