when the relation B−A+C = 1 holds. In this paper a formula is presented which evaluates this series in case when B −A+C is an integer. The formula expresses the infinite series as a linear combination of two Γ-terms with coefficients being finite hypergeometric 3F2 series. Algorithmical problems of summation of infinite hypergeometric series are considered in the light of the generalized formul...

Estimation of the quantile, mean, and variability of populations is generally carried out by means of sample estimates. Given normality of the parent population, the distribution of sample mean and sample variance is straightforward. However, when normality cannot be assumed, inference is usually based on approximations through the use of the Central Limit theorem. Furthermore, the data generat...

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of ...

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...