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By employing the linearization method and partial fractions, we examine a large class of nonterminating exotic 3 F 2 -series extended by five integer parameters. A general summation formula is proved, and several contiguous series are evaluated in closed form. [ABSTRACT FROM AUTHOR]

We evaluate, in closed forms, twelve infinite series that contain a free variable x and binomial coefficients ( 3 n + ϵ n) in the denominators. Several summation formulae resembling Gosper's sum are derived as consequences. [ABSTRACT FROM AUTHOR]

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either hand or machine calculations. Some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important feature of this approach is that there is no need to solve a system of linear equations or to use differentiations to find the unknown coefficients of the partial fractions. In order to study its potential application in mathematics education at the undergraduate level, a pilot study of tryout at the Hong Kong Institute of Education has been conducted. The data are collected via quizzes, questionnaires and face-to-face interviews. In this article, the results and implications will be discussed. In general, according to the responses and feedbacks from the instructors and students concerned, the improved Heaviside approach is suitable to be introduced at the undergraduate level, as an alternative to the method of undetermined coefficients described in common undergraduate mathematics textbooks. [ABSTRACT FROM PUBLISHER]

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear equations. Some examples of its applications are included. [ABSTRACT FROM AUTHOR]