About the Project
NIST

separation constant

AdvancedHelp

(0.001 seconds)

1—10 of 37 matching pages

1: 28.32 Mathematical Applications
The separated solutions V ( ξ , η ) = v ( ξ ) w ( η ) can be obtained from the modified Mathieu’s equation (28.20.1) for v and from Mathieu’s equation (28.2.1) for w , where a is the separation constant and q = 1 4 c 2 k 2 . … 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: 31.10 Integral Equations and Representations
Kernel Functions
where σ is a separation constant. …
31.10.19 𝒦 ( u , v , w ) = u 1 - γ v 1 - δ w 1 - ϵ 𝒞 1 - γ ( u σ 1 ) 𝒞 1 - δ ( v σ 2 ) 𝒞 1 - ϵ ( i w σ 1 + σ 2 ) ,
where σ 1 and σ 2 are separation constants. … and σ 1 and σ 2 are separation constants. …
3: 29.18 Mathematical Applications
29.18.7 d 2 u 3 d γ 2 + ( h - ν ( ν + 1 ) k 2 sn 2 ( γ , k ) ) u 3 = 0 ,
with separation constants h and ν . …
4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
and w 2 , w 3 satisfy (30.13.10) and (30.13.11), respectively, with γ 2 = - κ 2 c 2 0 and separation constants λ and μ 2 . …
5: Bibliography S
  • J. A. Stratton, P. M. Morse, L. J. Chu, and R. A. Hutner (1941) Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.
  • J. A. Stratton, P. M. Morse, L. J. Chu, J. D. C. Little, and F. J. Corbató (1956) Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients. Technology Press of M. I. T. and John Wiley & Sons, Inc., New York.
  • 6: 30.13 Wave Equation in Prolate Spheroidal Coordinates
    with γ 2 = κ 2 c 2 0 and separation constants λ and μ 2 . …
    7: 33.22 Particle Scattering and Atomic and Molecular Spectra
    With e denoting here the elementary charge, the Coulomb potential between two point particles with charges Z 1 e , Z 2 e and masses m 1 , m 2 separated by a distance s is V ( s ) = Z 1 Z 2 e 2 / ( 4 π ε 0 s ) = Z 1 Z 2 α c / s , where Z j are atomic numbers, ε 0 is the electric constant, α is the fine structure constant, and is the reduced Planck’s constant. The reduced mass is m = m 1 m 2 / ( m 1 + m 2 ) , and at energy of relative motion E with relative orbital angular momentum , the Schrödinger equation for the radial wave function w ( s ) is given by
    33.22.1 ( - 2 2 m ( d 2 d s 2 - ( + 1 ) s 2 ) + Z 1 Z 2 α c s ) w = E w ,
    8: 12.5 Integral Representations
    where the contour separates the poles of Γ ( t ) from those of Γ ( 1 2 + a - 2 t ) . … where the contour separates the poles of Γ ( t ) from those of Γ ( 1 2 - a - 2 t ) . …
    9: 15.6 Integral Representations
    In (15.6.6) the integration contour separates the poles of Γ ( a + t ) and Γ ( b + t ) from those of Γ ( - t ) , and ( - z ) t has its principal value. In (15.6.7) the integration contour separates the poles of Γ ( a + t ) and Γ ( b + t ) from those of Γ ( c - a - b - t ) and Γ ( - t ) , and ( 1 - z ) t has its principal value. …
    10: 13.4 Integral Representations
    where the contour of integration separates the poles of Γ ( a + t ) from those of Γ ( - t ) . … where the contour of integration separates the poles of Γ ( a + t ) Γ ( 1 + a - b + t ) from those of Γ ( - t ) . …