Theta and Riemann xi function representations from harmonic oscillator eigensolutions
arXiv:math-ph/0612086 · doi:10.1016/j.physleta.2006.10.055
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
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- Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
- Some applications of the Stieltjes constants
- On an integral involving the digamma function
- The difference between two Stieltjes constants
- A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
- A formula connecting the Bernoulli numbers with the Stieltjes constants
- Special functions and the Mellin transforms of Laguerre and Hermite functions
- Some integrals involving the Stieltjes constants:Part II
- Riemann Hypothesis, Modified Morse Potential and Supersymmetric Quantum Mechanics
- Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series