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ISBN: 1441970193 1441970207 Year: 2010 Publisher: New York, NY : Springer New York : Imprint: Springer,
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Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusing on the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differential Equations. A solutions manual is available online.
Differential equations. --- Electronic books. -- local. --- Hypergeometric functions --- Differential equations, Partial --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Numerical solutions --- 517.91 Differential equations --- Differential equations --- Mathematics. --- Difference equations. --- Functional equations. --- Functions of complex variables. --- Special functions. --- Ordinary Differential Equations. --- Special Functions. --- Functions of a Complex Variable. --- Difference and Functional Equations. --- Special functions --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Differential Equations. --- Functions, special. --- Hypergeometric functions. --- Numerical solutions.
Book
ISBN: 3642122299 9786613569622 3642122302 1280391707 Year: 2010 Publisher: Heidelberg : Springer,
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In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.
Bessel functions --- Hypergeometric functions --- Geometric function theory --- Inequalities (Mathematics) --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Operations Research --- Bessel functions. --- Hypergeometric functions. --- Geometric function theory. --- Function theory, Geometric --- Functions, Hypergeometric --- Cylindrical harmonics --- Mathematics. --- Difference equations. --- Functional equations. --- Functions of complex variables. --- Functions of real variables. --- Special functions. --- Special Functions. --- Functions of a Complex Variable. --- Real Functions. --- Difference and Functional Equations. --- Special functions --- Mathematical analysis --- Equations, Functional --- Functional analysis --- Real variables --- Functions of complex variables --- Complex variables --- Elliptic functions --- Functions of real variables --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Processes, Infinite --- Transcendental functions --- Hypergeometric series --- Bessel polynomials --- Harmonic analysis --- Harmonic functions --- Functions, special.
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