Theta and Riemann xi function representations from harmonic oscillator eigensolutions

Abstract

From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A key result provides a basis for generalizing the important Riemann-Siegel integral formula.

15 pages, no figures, appears in Phys. Lett. A

References in corpus (1)

• Special functions and the Mellin transforms of Laguerre and Hermite functions

Cited by in corpus (6)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
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• The difference between two Stieltjes constants
• A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
• Special functions and the Mellin transforms of Laguerre and Hermite functions
• Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series