Frullani integral In mathematics, Frullani integrals are a specific
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Frullani integral - Wikipedia
Frullani integral In mathematics, Frullani integrals are a specific type of improper integral named after the Italian mathematician Giuliano Frullani. The integrals are of the form where is a function defined for all non- negative real numbers that has a limit at , which we denote by . The following formula for their general solution holds under certain conditions: A simple proof of the formula can be arrived at by using the Fundamental theorem of calculus to express the integrand as an integral of : Proof and then use Fubini's theorem to interchange the two integrals: Note that the integral in the second line above has been taken over the interval , not . The formula can be used to derive an integral representation for the natural logarithm by letting and : The formula can also be generalized in several different ways. [1] G. Boros, Victor Hugo Moll, Irresistible Integrals (2004), pp. 98 Juan Arias-de-Reyna, On the Theorem of Frullani (https://www.ams.org/journals/pro c/1990-109-01/S0002-9939-1990-1007485-4/S000 Applications References 2-9939-1990-1007485-4.pdf) (PDF; 884 kB), Proc. A.M.S. 109 (1990), 165-175. ProofWiki, proof of Frullani's integral (http s://proofwiki.org/wiki/Frullani%27s_Integral #Proof) . 1. Bravo, Sergio; Gonzalez, Ivan; Kohl, Karen; Moll, Victor Hugo (21 January 2017). "Integrals of Frullani type and the method of brackets" (htt ps://www.degruyter.com/view/journals/math/ 15/1/article-p1.xml) . Open Mathematics. 15 (1). doi:10.1515/math-2017-0001 (https://doi.org/10.15 15%2Fmath-2017-0001) . Retrieved 17 June 2020. Retrieved from "https://en.wikipedia.org/w/index.php? title=Frullani_integral&oldid=1135793950" This page was last edited on 26 January 2023, at 22:11 (UTC). • Content is available under CC BY-SA 3.0 unless otherwise noted. Download 166.49 Kb. Do'stlaringiz bilan baham: |
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