in this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. the method is applied to a few test examples to illustrate the accuracy and the implementation of the method

We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such is find some infinite products whose integrals over suitable contours are still products. used here motivated by Rosengren's proof the Kanade-Russell identities.

Corresponding material in the book: Section 15.2, 15.3. Note: We are omitting the question types from the book that require three-dimensional visualization, i.e., those that require sketching figures in three dimensions to compute volumes. What students should definitely get: The procedure for computing double integrals over rectangles using iterated integrals, the procedure for computing doubl...

In this work, we present a computational method for solving double and triple integrals with variable limits of integrations which is based on Haar wavelets. This approach is the generalization and improvement of the methods [3]. The advantage of this new methods is its more efficient and simple applicability than the previous methods. Error analysis for the case of two dimension are considered...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

The triple integrals

In a recent paper [1] we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines. Here we show how to extend this algorithm to Feynman diagrams with massive propagators and arbitrary propagator powers. As applications, we present numeri...

In this paper Haar wavelets and hybrid functions have been applied for numerical solution of double and triple integrals with variable limits of integration. This approach is the generalization and improvement of the method [31] where the numerical method is only applicable to the integrals with constant limits. Apart from generalization of the method [31], the new approach has two major advant...