Special functions and the Mellin transforms of Laguerre and Hermite functions
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Mark W. Coffey
We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynomial or other factors of the Mellin transforms have zeros only on the critical line Re s = 1/2. We additionally present a simple-zero Proposition for the Mellin transform of the wavefunction of the D-dimensional hydrogenic atom. These results are of interest to several areas including quantum mechanics and analytic number theory.
© Oldenbourg Wissenschaftsverlag
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- Asymptotic estimates for a semigroup related to compressible viscous fluid flow
- Oscillation of first order neutral differential equations of Euler form
- WENO-TVD schemes for hyperbolic conservation laws
- Special functions and the Mellin transforms of Laguerre and Hermite functions
- On a class of extremal solutions of the nondegenerate matricial Carathéodory problem
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Articles in the same Issue
- Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points
- Asymptotic estimates for a semigroup related to compressible viscous fluid flow
- Oscillation of first order neutral differential equations of Euler form
- WENO-TVD schemes for hyperbolic conservation laws
- Special functions and the Mellin transforms of Laguerre and Hermite functions
- On a class of extremal solutions of the nondegenerate matricial Carathéodory problem
- Removable singularities of fully nonlinear elliptic equations
