scholarly journals Microwave Specific Attenuation by Oblate Spheroidal Raindrops: an Exact Analysis of TCS's in Terms of Spheroidal Wave Functions

1998 ◽  
Vol 18 ◽  
pp. 127-150 ◽  
Author(s):  
L. W. Li ◽  
T. S. Yeo ◽  
P. S. Kooi ◽  
M. S. Leong
Keyword(s):  
Wave Functions ◽  
Spheroidal Wave Functions ◽  
Exact Analysis ◽  
Specific Attenuation ◽  
Oblate Spheroidal

scholarly journals Product formulas and convolutions for the radial oblate spheroidal wave functions

1999 ◽  
Vol 6 (3) ◽  
pp. 347-362 ◽  
Author(s):  
William C. Connett ◽  
Clemens Markett ◽  
Alan L. Schwartz
Keyword(s):  
Wave Functions ◽  
Spheroidal Wave Functions ◽  
Oblate Spheroidal ◽  
Product Formulas

The oblate spheroidal wave functions

1950 ◽  
Vol 249 (4) ◽  
pp. 299-321 ◽  
Author(s):  
A. Leitner ◽  
R.D. Spence
Keyword(s):  
Wave Functions ◽  
Spheroidal Wave Functions ◽  
Oblate Spheroidal

scholarly journals Spheroidal wave-functions

1925 ◽  
Vol 107 (741) ◽  
pp. 43-60
Keyword(s):  
Wave Motion ◽  
Wave Length ◽  
Two Dimensions ◽  
Wave Functions ◽  
External Region ◽  
Spheroidal Wave Functions ◽  
Oblate Spheroidal ◽  
Usual Manner ◽  
Fundamental Vector ◽  
Velocity Of Propagation

The solution of problems relating to vibrations, in connection with spheroids— or, in two dimensions, elliptic cylinders—has hitherto only been attempted in one manner. If the vibrations have a time factor for their fundamental vector, of the form ℯ ipt , the equation of wave motion becomes, if ø is the fundamental vector, (∇ 2 + k 2 ) ø = 0 where the wave-length is 2π/ k ,and if C is the velocity of propagation of the wave in the external region, k = p/c . When oblate spheroidal co-ordinates are used, defined in terms of Cartesians by x= a √ { (1 + μ 2 ) (1 + ζ 2 ) } cos ω, y = a √ {1 - μ 2 ) (1 + ζ 2 ) } sin ω, z = a μζ, this can be transformed, after the usual manner, to ∂/∂μ (1 - μ 2 ) ∂ø/∂μ + ∂/∂ζ (1+ζ 2 ) ∂ø/∂ζ + k 2 a 2 (μ 2 + ζ 2 ) ø = 0, (1) when there is symmetry round the axis of z .

Prolate angular spheroidal wave functions

1983 ◽  
Vol 30 (2) ◽  
pp. 187-192 ◽  
Author(s):  
T.A. Beu ◽  
R.I. Câmpeanu
Keyword(s):  
Wave Functions ◽  
Spheroidal Wave Functions
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