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math-ph2013
Mellin transforms with only critical zeros: Chebyshev and Gegenbauer functions
Mark W. Coffey, Matthew C. Lettington
We consider the Mellin transforms of certain Chebyshev functions based upon the Chebyshev polynomials. We show that the transforms have polynomial factors whose zeros lie all on th…
math-ph2013
Mellin transforms with only critical zeros: Legendre functions
Mark W. Coffey, Matthew C. Lettington
We consider the Mellin transforms of certain Legendre functions based upon the ordinary and associated Legendre polynomials. We show that the transforms have polynomial factors who…