Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions
Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show how this...
Some inequalities of the incomplete gamma and related functions.
Some properties of the incomplete beta function ratio
Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions.