01258aam 2200373I 450 991070951100332120151026025822.0GOVPUB-C13-69771f6d5d6b56a5a54c8154a0af17c7(CKB)5470000002479895(OCoLC)926742475(EXLCZ)99547000000247989520151026d1985 ua 0engrdacontentrdamediardacarrierOM85 basic properties of optical materials /Albert FeldmanGaithersburg, MD :U.S. Dept. of Commerce, National Institute of Standards and Technology,1985.1 online resourceNBS special publication ;6971985.Contributed record: Metadata reviewed, not verified. Some fields updated by batch processes.Title from PDF title page.Includes bibliographical references.Feldman Albert1391920Feldman Albert1391920United States.National Bureau of Standards.NBSNBSGPOBOOK9910709511003321OM85 basic properties of optical materials3446115UNINA04439nam 22006735 450 991086313700332120251113190356.03-662-61550-910.1007/978-3-662-61550-8(CKB)4100000011528437(MiAaPQ)EBC6381292(DE-He213)978-3-662-61550-8(PPN)258059141(EXLCZ)99410000001152843720201027d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierMittag-Leffler Functions, Related Topics and Applications /by Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin2nd ed. 2020.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2020.1 online resource (XVI, 540 p. 22 illus., 11 illus. in color.) Springer Monographs in Mathematics,2196-99223-662-61549-5 Includes bibliographical references and index.Preface -- Introduction -- Overview on the Mittag-Leffler funtion -- Classical Mittag-Laffler function -- Two-parametric Mittag-Leffler functions with three parameters -- Multi-index and multi-variable Mittag-Leffler functions. - The Classical Wright function. - Applications to solution of fractional order equations. - Applications to deterministic models -- Applications to stochastic models. - Appendix A. The Eulerian functions -- Appendix B. Basic of Entire Functions -- Appendix C. Integral transforms -- Appendix D. Mellin-Barnes integral. - Appendix E. Elements of Fractional Calculus -- Appendix F. Higher transcendental functions -- References -- Index.The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.Springer Monographs in Mathematics,2196-9922Mathematical physicsSpecial functionsMathematical modelsIntegral equationsProbabilitiesMathematical PhysicsSpecial FunctionsMathematical Modeling and Industrial MathematicsIntegral EquationsProbability TheoryMathematical physics.Special functions.Mathematical models.Integral equations.Probabilities.Mathematical Physics.Special Functions.Mathematical Modeling and Industrial Mathematics.Integral Equations.Probability Theory.515.75Gorenflo Rudolf42618MiAaPQMiAaPQMiAaPQBOOK9910863137003321Mittag-Leffler Functions, Related Topics and Applications1749652UNINA