On the Results of Coffy and Moli
Anand G Puranik
Anand G Puranik, Department of Mathematics, Government Science College, Chitradurga (Karnataka), India.
Manuscript received on 14 January 2023 | Revised Manuscript received on 04 February 2023 | Manuscript Accepted on 15 April 2023 | Manuscript published on 30 April 2023 | PP: 8-11 | Volume-3 Issue-1, April 2023 | Retrieval Number: 100.1/ijam.A1142043123 | DOI: 10.54105/ijam.A1142.043123
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Abstract: The primary aim of this article is Generalization leading to search of integrals of the type∫ 𝒍𝒐𝒈𝑷 𝒍𝒐𝒈𝑸 𝒅𝒙 = ∫ 𝑭𝑮 𝒏𝒅𝒙 where both P, Q are functions of x only and also verification of results by using new trend. In this direction of verification, converting integrals into ordinary differential equations and finding the solutions, has significant trend and fresh impetus in the recent years. In this paper, along with the generalization of integrals, formation of ordinary differential equations and their solutions were also listed. Here in this article we obtained significant differential equations based on integrals of Russell [1], type. In the first part, generalizations of preliminary lemmas along with new integrals of logarithmic integrand were evaluated on the lines Mark Coffy [4]. Then first order linear differential equations were obtained for such integrals, to verify the truth of the solutions.
Keywords: Beta-functions, Definite Integrals, First order linear Differential Equations. Gamma-functions, Taylor Series, Ordinary Differential Equations.
Scope of the Article: Calculus and Analysis