001451336 000__ 04343cam\a2200493\a\4500
001451336 001__ 1451336
001451336 003__ OCoLC
001451336 005__ 20230310004655.0
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001451336 008__ 221126s2022\\\\sz\\\\\\ob\\\\001\0\eng\d
001451336 019__ $$a1350866343
001451336 020__ $$a9783031178719$$q(electronic bk.)
001451336 020__ $$a3031178718$$q(electronic bk.)
001451336 020__ $$z303117870X
001451336 020__ $$z9783031178702
001451336 0247_ $$a10.1007/978-3-031-17871-9$$2doi
001451336 035__ $$aSP(OCoLC)1351195570
001451336 040__ $$aEBLCP$$beng$$cEBLCP$$dGW5XE$$dYDX$$dEBLCP$$dOCLCF$$dUKAHL$$dOCLCQ
001451336 049__ $$aISEA
001451336 050_4 $$aQA351
001451336 08204 $$a515/.5$$223/eng/20221130
001451336 1001_ $$aRuffa, Anthony A.
001451336 24510 $$aInnovative integrals and their Applications.$$nI /$$cAnthony A. Ruffa, Bourama Toni.
001451336 260__ $$aCham :$$bSpringer,$$c2022.
001451336 300__ $$a1 online resource (325 p.).
001451336 4901_ $$aSTEAM-H
001451336 504__ $$aIncludes bibliographical references and index.
001451336 5050_ $$aPreface -- Chapter. 1. The Generalized Method of Exhaustion -- Chapter. 2. The Multivariate Power Substitution and its Variants -- Chapter. 3. Additional Multivariate Substitution Variants -- Chapter. 4. Miscellaneous Integral Identities -- Chapter. 5. The Exponential Integral Function, the Sine Integral and Cosine Integrals -- Chapter. 6. The Riemann Zeta Function and the Hurwitz Zeta Function -- Chapter. 7. Engineering Applications -- Bibliography -- Index.
001451336 506__ $$aAccess limited to authorized users.
001451336 520__ $$aThis book develops integral identities, mostly involving multidimensional functions and infinite limits of integration, whose evaluations are intractable by common means. It exposes a methodology based on the multivariate power substitution and its variants, assisted by the software tool Mathematica. The approaches introduced comprise the generalized method of exhaustion, the multivariate power substitution and its variants, and the use of permutation symmetry to evaluate definite integrals, which are very important both in their own right, and as necessary intermediate steps towards more involved computation. A key tenet is that such approaches work best when applied to integrals having certain characteristics as a starting point. Most integrals, if used as a starting point, will lead to no result at all, or will lead to a known result. However, there is a special class of integrals (i.e., innovative integrals) which, if used as a starting point for such approaches, will lead to new and useful results, and can also enable the reader to generate many other new results that are not in the book. The reader will find a myriad of novel approaches for evaluating integrals, with a focus on tools such as Mathematica as a means of obtaining useful results, and also checking whether they are already known. Results presented involve the gamma function, the hypergeometric functions, the complementary error function, the exponential integral function, the Riemann zeta function, and others that will be introduced as they arise. The book concludes with selected engineering applications, e.g., involving wave propagation, antenna theory, non-Gaussian and weighted Gaussian distributions, and other areas. The intended audience comprises junior and senior sciences majors planning to continue in the pure and applied sciences at the graduate level, graduate students in mathematics and the sciences, and junior and established researchers in mathematical physics, engineering, and mathematics. Indeed, the pedagogical inclination of the exposition will have students work out, understand, and efficiently use multidimensional integrals from first principles.
001451336 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 30, 2022).
001451336 650_0 $$aFunctions, Special.
001451336 650_0 $$aIntegral equations.
001451336 655_0 $$aElectronic books.
001451336 7001_ $$aToni, Bourama.
001451336 77608 $$iPrint version:$$aRuffa, Anthony A.$$tInnovative Integrals and Their Applications I$$dCham : Springer International Publishing AG,c2022$$z9783031178702
001451336 830_0 $$aSTEAM-H (Series)
001451336 852__ $$bebk
001451336 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-17871-9$$zOnline Access$$91397441.1
001451336 909CO $$ooai:library.usi.edu:1451336$$pGLOBAL_SET
001451336 980__ $$aBIB
001451336 980__ $$aEBOOK
001451336 982__ $$aEbook
001451336 983__ $$aOnline
001451336 994__ $$a92$$bISE