A new proof of Watson's theorem for the series 3F2(1)

We give a new proof of the classical Watson theorem for the summation of a 3F2 hypergeometric series of unit argument. The proof relies on the two well-known Gauss summation theorems for the 2F1 function

A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach

The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach

On a new class of summation formulae involving the Laguerre polynomial

By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form

An extension of Saalschütz's summation theorem for the series _<i>r</i>+3F_<i>r</i>+2

The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear]

On two Thomae-type transformations for hypergeometric series with integral parameter differences

We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given

Analisis Lokasi Sekolah SMA yang Ideal di Kabupaten Bone Bolango dengan Sistem Informasi Geografis

In Indonesia, the problem of educational equity is still a serious problem, there are still few schools and the distance between most students' homes and schools is quite far from the school location. This study aims to determine the location of the ideal high school in Bone Bolango Regency by using a Geographic Information System. The location of this research was carried out in Bone Bolango Regency, the schools studied were SMA Negeri 1 Tapa, SMA Negeri 1 Kabila, SMA Negeri 1 Suwawa, SMA Negeri 1 Suwawa Timur, SMA Negeri 1 Bone, SMA Negeri 1 Bone Pantai, SMA Negeri 1 Bulango Ulu. , SMA Negeri 1 Pinogu, SMAS Terpadu Wirabakti. The method used in the research is a survey, interviews and then given a score with predetermined criteria. Primary data is obtained directly through observations, field measurements and interpretation of satellite imagery. In this study, the primary data were land area for education units, slope, accessibility, free of disasters and landslides, educational reach, and number of students. Secondary data is obtained from information, statistical data and data derived from existing field data. In this study the secondary data is the distribution of high school schools. The time of the study was conducted for 6 months from February to July. The research results are based on parameters with certain criteria, namely land area for education units, slope, accessibility, free of disasters and landslides, and educational reach. Then the five parameters are scored and the results are overlaid into an ideal school map

Comments on "New hypergeometric identities arising from Gauss’s second summation theorem"

In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269–274] obtained a general transfor- mation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities not previously recorded in the literature were then deduced by application of Gauss’ second summation theorem and other known hypergeometric summa- tion theorems. However, many of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities