Mellin Transforms with a Complex Parameter

1994 ◽  
pp. 183-192
Author(s):  
Richard J. Sasiela
Keyword(s):  
Complex Parameter ◽  
Mellin Transforms

The Complex Parameter Rao Test

2016 ◽  
Vol 64 (24) ◽  
pp. 6580-6588 ◽  
Author(s):  
Steven Kay ◽  
Zhenghan Zhu
Keyword(s):  
Complex Parameter ◽  
Rao Test

On Hankel and Mellin transforms

1978 ◽  
Vol 9 (2) ◽  
pp. 139-145
Author(s):  
N. Mullineux ◽  
J.R. Reed
Keyword(s):  
Mellin Transforms

Mellin transforms over Cayley-Dickson algebras

2008 ◽  
Vol 77 (2) ◽  
pp. 249-253
Author(s):  
S. V. Lyudkovskii
Keyword(s):  
Mellin Transforms

scholarly journals Generalised sturm-liouville expansions in series of pairs of related functions

1927 ◽  
Vol 115 (770) ◽  
pp. 184-198 ◽  
Keyword(s):  
Boundary Conditions ◽  
Differentiable Function ◽  
Real Variable ◽  
Complex Parameter ◽  
The Real ◽  
The Earth ◽  
In Series ◽  
Sturm Liouville

The expansions here developed are required for the author’s discussion of "Meteorological Perturbations of Tides and Currents in an Unlimited Channel rotating with the Earth” ( v. supra , p. 170). Let η ( x ) be a real differentiable function of x defined in the range 0 ≼ x ≼ 1, and satisfying the condition η ( x ) > c > 0 for all such x . Let ϕ λ ( x ) and ψ λ ( x ) be functions of the real variable x and the complex parameter λ , defined in the above range by the equations d / dx [ η ( x ) dϕ λ ( x )/ dx ] + ( λ + iγ ) ϕ λ ( x ) = -1, d / dx [ η ( x ) dψ λ ( x )/ dx ] + ( λ + iγ ) ψ λ ( x ) = -1 (1) together with the boundary conditions ϕ' λ (0) = 0, ψ' λ (0) = 0, ϕ' λ (1) = 0, ψ λ (1) = 0, (2) γ being a prescribed constant.

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