LEADER 04897nam 22006735 450 001 9910631078203321 005 20250515004813.0 010 $a3-031-17871-8 024 7 $a10.1007/978-3-031-17871-9 035 $a(MiAaPQ)EBC7140451 035 $a(Au-PeEL)EBL7140451 035 $a(CKB)25332791600041 035 $a(PPN)266352588 035 $a(DE-He213)978-3-031-17871-9 035 $a(EXLCZ)9925332791600041 100 $a20221114d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInnovative Integrals and Their Applications I /$fby Anthony A. Ruffa, Bourama Toni 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (325 pages) 225 1 $aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,$x2520-1948 311 08$aPrint version: Ruffa, Anthony A. Innovative Integrals and Their Applications I Cham : Springer International Publishing AG,c2022 9783031178702 327 $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. 330 $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, willlead 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. 410 0$aSTEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health,$x2520-1948 606 $aFunctions, Special 606 $aIntegral equations 606 $aAlgebraic fields 606 $aPolynomials 606 $aMathematical analysis 606 $aSpecial Functions 606 $aIntegral Equations 606 $aField Theory and Polynomials 606 $aIntegral Transforms and Operational Calculus 615 0$aFunctions, Special. 615 0$aIntegral equations. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aMathematical analysis. 615 14$aSpecial Functions. 615 24$aIntegral Equations. 615 24$aField Theory and Polynomials. 615 24$aIntegral Transforms and Operational Calculus. 676 $a515.5 676 $a515.43 700 $aRuffa$b Anthony A.$01264622 702 $aToni$b Bourama 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910631078203321 996 $aInnovative integrals and their applications I$93083134 997 $aUNINA