## Universal Formulas In Integral And Fractional Differential Calculus

**Author**: Khavtgai Namsrai

**Publisher:**World Scientific

**ISBN:**981467561X

**Size**: 27.27 MB

**Format:**PDF, ePub, Docs

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' This reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators. Despite the great success of numerical calculations due to computer technology, analytical calculations still play a vital role in the study of new, as yet unexplored, areas of mathematics, physics and other branches of sciences. Readers, including non-specialists, can obtain themselves universal formulas and define new special functions in integral and series representations by using the methods expounded in this book. This applies to anyone utilizing analytical calculations in their studies. Contents:Mathematical PreparationCalculation of Integrals Containing Trigonometric and Power FunctionsIntegrals Involving xγ, (p + txp)–λ Sine and Cosine FunctionsDerivation of General Formulas for Integrals Involving Powers of x, (a + bx)-Type Binomials and Trigonometric FunctionsIntegrals Involving xγ, 1/(p + txp)–λ, exp[–axγ] and Trigonometric FunctionsIntegrals Containing Bessel FunctionsIntegrals Involving the Neumann Function Nσ(x)Integrals Containing Other Cylindrical and Special FunctionsIntegrals Involving Two Trigonometric FunctionsDerivation of Universal Formulas for Calculation of Fractional Derivatives and Inverse Operators Readership: Undergraduate and graduate students interested in analytic calculations in integral calculus. Researchers from the fields of modern mathematical analysis, theoretical physics and engineering. Non-experts interested in integrals, fractional derivatives and inverse operators. Key Features:Content in this book is easy to readHas simple tables of integration and taking fractional derivatives and calculating complicated inverse operatorsMost valuable tip from the book is a simple and nice way to perform integration showing it as a design culture but not as tedious workKeywords:Mellin Representation;Contour Integration;Analytic Continuation;Taking Residue;L''Hôpital''s Rule;Gamma Function;Psi-Function;Exponential Function;Neumann;Trigonometric;Cylindrical;Struve;Modified Struve;Bessel and Modified Bessel Functions;Probability Integrals;Integral of Frenal;General Formulas for Taking Integrals;Fractional Derivatives;Inverse Operators;Euler Number'