Article ID: MTJPAM-D-25-00273

Title: Quadrature processes and numerical computation of the two dimensional exponential integrals

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-25-00273; Volume 7 / Issue 3 / Year 2025, Pages 114-129

Document Type: Research Paper

Author(s): ‪Gradimir V. Milovanović ^a

^aSerbian Academy of Sciences and Arts, Kneza Mihaila 35, 11000 Beograd, Serbia — University of Niš, Faculty of Sciences and Mathematics, 18000 Niš, Serbia

Received: 12 November 2025, Accepted: 15 January 2026, Published: 9 May 2026

Corresponding Author: Gradimir V. Milovanović (Email address: gvm@mi.sanu.ac.rs)

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Abstract

Integral representations of two dimensional exponential integral (TDEI) functions and their numerical computation based on quadrature processes are treated. In addition to a general brief description of important quadrature processes, including some historical details, three methods for numerical calculation of TDEI functions are presented in particular. Precisely, the construction and application of the truncated Gauss-Christoffel quadrature formulas, the composite trapezoidal rule, and the method of integration between zeros of the integrand to the calculation of the values of TDEI functions in various situations are given. A series of numerical examples are given, including error analysis.

Keywords: Two dimensional exponential integral, quadrature process, trapezoidal rule, Gaussian quadrature formula, double-exponential transformation, orthogonality, three-term recurrence relation

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