About the Project
NIST

Whittaker equation

AdvancedHelp

(0.002 seconds)

1—10 of 58 matching pages

1: 28.32 Mathematical Applications
§28.32(ii) Paraboloidal Coordinates
is separated in this system, each of the separated equations can be reduced to the Whittaker–Hill equation (28.31.1), in which A , B are separation constants. …
2: 13.14 Definitions and Basic Properties
§13.14(i) Differential Equation
Whittaker’s Equation
Standard solutions are: …
§13.14(v) Numerically Satisfactory Solutions
3: 13.28 Physical Applications
and V κ , μ ( j ) ( z ) , j = 1 , 2 , denotes any pair of solutions of Whittaker’s equation (13.14.1). …
4: Bibliography U
  • K. M. Urwin and F. M. Arscott (1970) Theory of the Whittaker-Hill equation. Proc. Roy. Soc. Edinburgh Sect. A 69, pp. 28–44.
  • 5: 28.31 Equations of Whittaker–Hill and Ince
    §28.31 Equations of Whittaker–Hill and Ince
    §28.31(i) Whittaker–Hill Equation
    and constant values of A , B , k , and c , is called the Equation of Whittaker–Hill. …
    6: 28.34 Methods of Computation
  • (f)

    Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

  • 7: 13.27 Mathematical Applications
    For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i).
    8: 23.3 Differential Equations
    §23.3 Differential Equations
    The lattice roots satisfy the cubic equation
    §23.3(ii) Differential Equations and Derivatives
    9: Bibliography
  • F. M. Arscott (1967) The Whittaker-Hill equation and the wave equation in paraboloidal co-ordinates. Proc. Roy. Soc. Edinburgh Sect. A 67, pp. 265–276.
  • 10: 32.10 Special Function Solutions
    §32.10(v) Fifth Painlevé Equation