An explicit expression for the autocovariance function of *X* on the axes is provided. With Yule–Walker equations, this facilitates the computation of the autocovariance function everywhere, at all integer points of the plane. In addition, all situations are described where different parameters determine the same autocovariance function of *X*.

PDF XML]]>An explicit expression for the autocovariance function of *X* on the axes is provided. With Yule–Walker equations, this facilitates the computation of the autocovariance function everywhere, at all integer points of the plane. In addition, all situations are described where different parameters determine the same autocovariance function of *X*.

PDF XML]]>This paper introduces novel formulas for binomial moments in the form of *polynomials in the variance* rather than in the success probability. The obtained formulas are arguably better structured, simpler and superior in their numerical properties compared to prior works. In addition, the paper presents algorithms to derive these formulas along with working implementation in Python’s symbolic algebra package.

The novel approach is a combinatorial argument coupled with clever algebraic simplifications which rely on symmetrization theory. As an interesting byproduct *asymptotically sharp estimates for central binomial moments* are established, improving upon previously known partial results.

PDF XML]]>This paper introduces novel formulas for binomial moments in the form of *polynomials in the variance* rather than in the success probability. The obtained formulas are arguably better structured, simpler and superior in their numerical properties compared to prior works. In addition, the paper presents algorithms to derive these formulas along with working implementation in Python’s symbolic algebra package.

The novel approach is a combinatorial argument coupled with clever algebraic simplifications which rely on symmetrization theory. As an interesting byproduct *asymptotically sharp estimates for central binomial moments* are established, improving upon previously known partial results.

PDF XML]]>