Convergence and Computation of a Class of Generalized Integrals

2019/12/09 by Haoding Meng, Meng, Haoding
Mathematics · #97I50 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.1912.03852

openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, we discuss the convergence and divergence of generalized integrals,∫₀^+∞\fracsin^bxx^adx(aεR⁺,bεN⁺), and use the transformation method, the partial integration method, the mathematical induction method and the complex variable residual method to derive the calculation formulas of the two types of integrals. The calculation formulas of the two types of integrals are unified. Finally, the convergence criterion and the unified calculation formula of generalized integrals of∫₀^+∞\fracsin^bxx^adxare obtained.

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