Download or read book Generalized Associated Legendre Functions and Their Applications written by Nina Opanasivna Virchenko and published by World Scientific. This book was released on 2001 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ?Fq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm, n?(z) and Qm, n?(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm, n?(z) and Qm, n?(z), the classes of dual and triple integral equations associated with the function Pm, n-1/2+i?(chà) etc.

Download or read book Table of Legendre Polynomials Pn cos theta for N written by W. Lane and published by . This book was released on 1947 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Engineering Mathematics written by R. K. Jain and published by Alpha Science Int'l Ltd.. This book was released on 2007 with total page 1168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based on the experience and notes of the authors while teaching mathematics courses to engineering students at the Indian Institute of Technology, New Delhi. It covers syllabi of two core courses in mathematics for engineering students.

Download or read book Applied Analysis by the Hilbert Space Method written by Samuel S. Holland and published by Courier Corporation. This book was released on 2012-05-04 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.

Download or read book Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica written by Kuzman Adzievski and published by CRC Press. This book was released on 2016-04-19 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs). The text represents a new approach to PDEs at the undergraduate level by presenting computation as an integral part of the study of differential equations. The authors use the computer software Mathematica (R) along with graphics to improve understanding and interpretation of concepts. The book also presents solutions to selected examples as well as exercises in each chapter. Topics include Laplace and Fourier transforms as well as Sturm-Liuville Boundary Value Problems.

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Download or read book Ordinary and Partial Differential Equations 20th Edition written by Raisinghania M.D. and published by S. Chand Publishing. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-acclaimed book, now in its twentieth edition, continues to offer an in-depth presentation of the fundamental concepts and their applications of ordinary and partial differential equations providing systematic solution techniques. The book provides step-by-step proofs of theorems to enhance students' problem-solving skill and includes plenty of carefully chosen solved examples to illustrate the concepts discussed.

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Download or read book Library of Congress Subject Headings written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1980 with total page 1314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Library of Congress Subject Headings written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1991 with total page 1692 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis And Differential Equations written by Odile Pons and published by World Scientific Publishing Company. This book was released on 2015-01-19 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered.It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.

Download or read book Analysis And Differential Equations Second Edition written by Odile Pons and published by World Scientific. This book was released on 2022-12-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

Download or read book ABSTRACT ALGEBRA DIFFERENTIAL EQUATION FOURIER SERIES written by HARI KISHAN and published by Ram Prasad Publications(R.P.H.). This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT ALGEBRA UNIT-I 1. Group Automorphism, Inner Automorphism, Group of Automorphisms 1-22 Introduction 1; Homomorphism of Group 1; Types of Homomorphism 1; Kernel of a Homomorphism 3; Some Theorems (Properties of Group Homomorphism) 3; Isomorphism of Groups 3; Fundamental Theorem of Homomorphism of Groups 3; More Properties of Group Homomorphism 4; Automorphism of a Group 4; Inner Automorphism 8; Theorem 4; Definition of Inner Automorphism 8; Centre of a Group 9; Group of Automorphisms 12; Group of Automorphisms of a Cyclic Group 14. 2. Cayley's Theorem 23-32 Permutation Groups and Transformations 23; Equality of Two Permutations 24; Identity Permutations 24; Cayley’s Theorem for Finite Group 25; Regular Permutation Group 26; Cayley’s Theorem for Infinite Group 26. 3. Counting Principle 33-44 Conjugate Elements and Conjugacy Relation 33; Conjugate Classes 33; Conjugate Subgroups 33; Conjugate Class of a Subgroup 34; Self Conjugate Elements 34; Normalizer or Centralizer of an Element 34; Normalizer of a Subgroup of a Group 34; Self-Conjugate Subgroups 34; Counting Principle 34. UNIT-II 4. Introduction to Rings and Subrings 45-72 Introduction 45; Ring 45; Examples of a Ring 46; Properties of a Ring 46; Types of Rings 46; Some Properties of a Ring 61; Integral Multiples of the Elements of a Ring 63; Some Special Kinds of Ring 63; Cancellation Laws in a Ring 65; Invertible Elements in a Ring with Unity 66; Division Rings or Skew Field 67; Quotient Ring or Factor Ring or Ring of Residue Classes 67; Subrings 69; Smallest Subring 72. 5. Integral Domain 73-84 Integral Domain 73; Sub-domain 74; Ordered Integral Domain 75; Inequalities 76; Well-ordered 76; Field 76; Some Theorems 76; The Characteristic of a Ring 78. 6. Ideals 85-100 Ideal 85; Theorem 85; Improper and Proper Ideals 86;Unit and Zero Ideals 86; Some Theorems 89; Smallest Ideal Containing a given Subset of a Ring 91; Principal Ideal 91; Principal Ideal Ring (or Principal Ideal Domain) 91; Prime Ideal 91; Maximal Ideal 92; Minimal Ideal 93; Sum of Two Ideals 93; Theorems 93; Product of Two Ideals 94; Important Theorems 94. DIFFERENTIAL EQUATIONS & FOURIER SERIES UNIT-III 1. Series Solutions of Differential Equations : Power Series Method 1-33 Power Series Method 1; Analytic or Regular or Holomorphic Function 1; Singular Point of the Differential Equation 1; Power Series 2; General Method for Solving a Differential Equation by Power Series Method 2; Frobenius Method 9; When Two Roots of Indicial Equation are Unequal and Differ by a Quantity not an Integer 10; Roots of the Indicial Equation Unequal and Differing by an Integer 17; When Roots of Indicial Equation are Equal 23; Series Solution Near an Ordinary Point (Power Series Method) 28. 2. Legendre’s Equation, Legendre’s Polynomial, Generating Function, Recurrence Formulae and Orthogonal Legendre’s Polynomials 34-78 Legendre’s Equation 34; Solution of Legendre’s Equation 34; Legendre’s Functions and its Properties 36; Legendre’s Functions 36; Legendre’s Function of the First Kind 37; Legendre’s Function of the Second Kind 37; Another Form of Legendre’s Polynomial Pn(x) 37; General Solution of Legendre’s Equation 39; Associated Legendre’s Functions 39; Generating Function for Legendre’s Polynomial 40; Orthogonal Properties of Legendre’s Polynomials 49; Recurrence Formulae 51; Beltrami’s Result 53; Christoffel’s Expansion Formula 54; Christoffel’s Summation Formula 55; Rodrigue’s Formula Pn(x) 65; Laplace’s Integral for Pn(x) 67; Some Bounds on Pn(x) 68. 3. Bessel’s Equation, Recurrence Formula 79-106 Bessel’s Equation 79; Solution of Bessel’s Equation 79, Bessel’s Functions 81; Bessel’s Function of the First Kind of Order n (or Index n) 81; Bessel’s Function of the Second Kind of Order n (or Neumann's Function) 82; General Solution of Bessel’s Equation 82; Integration of Bessel’s Equation for n = 0 and Bessel’s Functions of Zeroeth Order 82; Linear Dependence of Bessel Functions Jn(x) and J-n(x) 84; Recurrence Relations for Jn(x) 84; Elementary Functions 90. UNIT-IV 4. Fourier Series 107-134 Introduction 107; Periodic Function 107; Even and Odd Functions 107; Fourier Series for Even and Odd Functions 108; Euler’s Formulae 109; Orthogonal Functions 109; Important Definite Integrals 110; To Determine the Fourier Coefficients a0, an and bn 110; Dirichlet Conditions 122; Fourier Series for Discontinuous Functions 122; Change of Interval 127. 5. Half Range Fourier Sine and Cosine Series 135-152 Half Range Series : Fourier Sine and Cosine Series 135; Parseval’s Theorem 143; Complex Form of Fourier Series 146.

Download or read book Advanced Differential Equations written by M.D.Raisinghania and published by S. Chand Publishing. This book was released on 1995-03 with total page 1366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is especially prepared for B.A., B.Sc. and honours (Mathematics and Physics), M.A/M.Sc. (Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., AMIE, GATE, and other competitve exams.Almost all the chapters have been rewritten so that in the present form, the reader will not find any difficulty in understanding the subject matter.The matter of the previous edition has been re-organised so that now each topic gets its proper place in the book.More solved examples have been added so that now each topic gets its proper place in the book. References to the latest papers of various universities and I.A.S. examination have been made at proper places.