In the paper, authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine tangent, composite incomplete gamma function with hyperbolic sine, in terms first kind Stirling numbers, apply a newly established expansion to derive closed-form formula specific partial Bell polynomials representation generalized logsine function, deduce combinatorial involving...

This paper develops and compares the MAP and MMSE estimators for spherically-contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closed-form using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for t...

In a recent paper in this journal, Gautschi et al. [W. Gautschi, F.E. Harris, N.M. Temme, Expansions of the exponential integral in incomplete Gamma functions, Appl. Math. Lett. 16 (2003) 1095–1099] presented an interesting expansion formula for the exponential integral E1(z) in a series of the incomplete Gamma function γ (α, z). Their investigation was motivated by a search for better methods ...

Using a contour integral method, the de Montmort-Prudnikov sum is extended to derive new series representation involving incomplete gamma function. The uniformly convergent and completely analytical, which can be evaluated for general complex ranges of parameters involved. Applications evaluations this formula are discussed.