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Special Functions and Orthogonal Polynomials
(308 Pages). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.
Special Functions
(Hardcover). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.
Generalized Associated Legendre Functions And Their Applications
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 ρFq, 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...
Tables of Normalized Associated Legendre Polynomials
Tables of Normalized Associated Legendre Polynomials (1962) helps to resolve many problems in which a role is played by functions defined on the surface of a sphere, to write the functions as series in an orthogonal system of functions.
Tables of The Legendre Functions P—1⁄2+it(x)
Tables of the Legendre Functions P–1⁄2+iτ (X), Part I tabulates in detail the Legendre spherical functions of the first kind Pv(x) with complex index v = – 1⁄2 + iτ and real values of X > – 1. P–1⁄2+iτ (X) plays an important role in mathematical physics and are used in solving boundary value problems in potential theory for domains bounded by cones, hyperboloids of revolution, two intersecting spheres, or other second order surfaces. These Legendre functions are also of theoretical interest in connection with the Meler-Fok integral expansion. This book is devoted to the tables of P–1⁄2+iτ (X) and coefficients in the asymptotic formula. Some properties of the functions P–1⁄2+iτ (X) and description of the tables are also discussed. This publication is a good source for mathematical physicists and students conducting work on Legendre functions P–1⁄2+iτ (X).
An Algorithm for Calculating Smarandache's Function and Wich Using Legendre's Formula
The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.
Legendre Polynomials and Functions
This book provides an easy to follow study on Legendre Polynomials and Functions. It is also written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Legendre Polynomials and Functions that very often occur in engineering, physics, mathematics and applied sciences. I have collected many problems and gave numerous solved examples on the subject that might help the reader getting on-hand experience with the techniques presented in this note. It is hoped that this work will give some motivation to the reader to dig a bit further in the subject.
Special Functions of Mathematics for Engineers
Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.
Handbook of Mathematical Functions
An extensive summary of mathematical functions that occur in physical and engineering problems
