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• 1. Algebraic and analytic methods Ranjan Roy, Frank W. J. Olver, Richard A. Askey and Roderick S. C. Wong--
• 2. Asymptotic approximations Frank W. J. Olver and Roderick S. C. Wong--
• 3. Numerical methods Nico M. Temme--
• 4. Elementary functions Ranjan Roy and Frank W. J. Olver--
• 5. Gamma function Richard A. Askey and Ranjan Roy--
• 6. Exponential, logarithmic, sine and cosine integrals Nico M. Temme--
• 7. Error functions, Dawson's and Fresnel integrals Nico M. Temme--
• 8. Incomplete gamma and related functions Richard B. Paris--
• 9. Airy and related functions Frank W. J. Olver--
• 10. Bessel functions Frank W. J. Olver and Leonard C. Maximon--
• 11. Struve and related functions Richard B. Paris--
• 12. Parabolic cylinder functions Nico M. Temme--
• 13. Confluent hypergeometric functions Adri B. Olde Daalhuis--
• 14. Legendre and related functions T. Mark Dunster--
• 15. Hypergeometric function Adri B. Olde Daalhuis--
• 16. Generalized hypergeometric functions and Meijer G-function Richard A. Askey and Adri B. Olde Daalhuis--
• 17. q-Hypergeometric and related functions George E. Andrews--
• 18. Orthogonal polynomials Tom H. Koornwinder, Roderick S. C. Wong, Roelof Koekoek and Rene F. Swarttouw--
• 19. Elliptic integrals Bille C. Carlson--
• 20. Theta functions William P. Reinhardt and Peter L. Walker--
• 21. Multidimensional theta functions Bernard Deconinck--
• 22. Jacobian elliptic functions William P. Reinhardt and Peter L. Walker--
• 23. Weierstrass elliptic and modular functions William P. Reinhardt and Peter L. Walker--
• 24. Bernoulli and Euler polynomials Karl Dilcher--
• 25. Zeta and related functions Tom M. Apostol--
• 26. Combinatorial analysis David M. Bressoud--
• 27. Functions of number theory Tom M. Apostol--
• 28. Mathieu functions and Hill's equation Gerhard Wolf--
• 29. Lame functions Hans Volkmer--
• 30. Spheroidal wave functions Hans Volkmer--
• 31. Heun functions Brian D. Sleeman and Vadim Kuznetsov--
• 32. Painleve transcendents Peter A. Clarkson--
• 33. Coulomb functions Ian J. Thompson--
• 34. 3j, 6j, 9j symbols Leonard C. Maximon--
• 35. Functions of matrix argument Donald St. P. Richards--
• 36. Integrals with coalescing saddles Michael V. Berry and Chris Howls.
• (source: Nielsen Book Data)

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full colour, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Includes a DVD with a searchable PDF of each chapter.
(source: Nielsen Book Data)

• Preface.- The Constant Function c.- The Factorial Function n!.- The Zeta Numbers and Related Functions.- The Bernoulli Numbers Bn.- The Euler Numbers En.- The Bionmial Coefficients.- The Linear Function bx + c and Its Reciprocal.- Modifying Functions.- The Heaviside and Dirac Functions.- The Integer Powers xn and (bx + c)n.- The Square-Root Function and Its Reciprocal.- The Noninteger Power xv.- The Semielliptic Function and Its Reciprocal.- The (b/a)square root of x2 +- a2 Functions and Their Reciprocals.- The Quadratic Function ax + bx + c and Its Reciprocal.- The Cubic Function x3 + bx + c.- Polynomial Functions.- The Pochhammer Polynomials (x)n.- The Bernoulli Polynomials Bn(x).- The Euler Polynomials En(x).- The Legendre Polynomials Pn(x).- The Chebyshev Polynomials Tn(x) and Un(x).- The Laguerre Polynomials Ln(x).- The Hermite Polynomials Hn(x).- The Logarithmic Function ln(x).- The Exponential Function exp(x).- Exponential of Powers.- The Hyperbolic Cosine cosh(x). and Sine sinh(x) Functions.- The Hyperbolic Secant and Cosecant Functions.- The Inverse Hyperbolic Functions.- The Cosine cox(x) and Sine sin(x) Functions.- The Secant sec(x) and Cosecant csc(x) Fucntions.- The Tangent tan(x) and Cotangent cot(x) Functions.- The Inverse Circular Functions.- Periodic Functions.- The Exponential Integrals Ei(x) and Ein(x).- Sine and Cosine Integrals.- The Fresnel Integrals C(x) and S(x).- The Error Function erf(x) and Its Complement erfc(x).- The exp(x)erfc(square root of x) and Related Functions.- Dawson's Integral daw(x).- The Gamma Function.- The Digamma Function.- The Incomplete Gamma Functions.- The Parabolic Cylinder Function Dv(x).- The Kummer Function M(a, c, x).- The Tricomi Function U(a, c, x).- The Modified Bessel Functions In(x) of Integer Order.- The Modified Bessel Functions of In(x) Arbitrary Order.- The Macdonald Function Kv(x).- The Bessel Functions Jn(x) of Integer Order.- The Bessel Functions Jv(x) of Arbitrary Order.- The Neumann Function Yv(x). The Kelvin Functions.- The Airy Functions Ai(x) and Bi(x).- The Struve Function hv(x).- The Incomplete Beta Function.- The Legendre Functions Pv(x) and Qv(x).- The Gauss Hypergeometric Function F(a, b, c, x).- The Complete Elliptic Integrals K(k) and E(k).- The Incomplete Elliptic Integrals.- The Jacobian Elliptic Functions.- The Hurwitz Function.- Appendix A: Useful Data.- Appendix B: Bibliography.- Appendix C: Equator, The Atlas Function Calculator.- Symbol Index.- Subject Index.
• (source: Nielsen Book Data)

This second edition of "An Atlas of Functions, with Equator, the Atlas Function Calculator", provides comprehensive information on several hundred functions or function families, of interest to all those scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, as well as many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while utility is stressed throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in 2 or 3 dimensions depict their shape and qualitative features and flesh out the reader's familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family. Features that make the Atlas an invaluable reference tool, yet simple to use, include: full coverage of those functions - elementary and 'special' - that meet everyday needs; a standardized chapter format, making it easy to locate needed information on such aspects as - nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus; and, extensive cross-referencing and comprehensive indexing, with useful appendices. It also features the inclusion of innovative software - Equator, the Atlas Function Calculator - on a CD with the print book obviating the need for tables or programming to find numerical values (once installed onto your Windows-based PC, this unique function calculator generates precise function values on demand). It also includes new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.
(source: Nielsen Book Data)

• Preface--
• 1. Elementary bounds for univalent functions--
• 2. The growth of finitely mean valent functions--
• 3. Means and coefficients--
• 4. Symmetrization--
• 5. Circumferentially mean p-valent functions--
• 6. Differences of successive coefficients--
• 7. The Lowner theory--
• 8. De Branges' Theorem-- Bibliography-- Index.
• (source: Nielsen Book Data)

The class of multivalent functions is an important one in complex analysis. They occur for example in the proof of De Branges' theorem which, in 1985, settled the long-standing Bieberbach conjecture. The second edition of Professor Hayman's celebrated book contains a full and self-contained proof of this result, with a chapter devoted to it. Another chapter deals with coefficient differences. It has been updated in several other ways, with theorems of Baernstein and Pommerenke on univalent functions of restricted growth, and an account of the theory of mean p-valent functions. In addition, many of the original proofs have been simplified. Each chapter contains examples and exercises of varying degrees of difficulty designed both to test understanding and illustrate the material. Consequently it will be useful for graduate students, and essential for specialists in complex function theory.
(source: Nielsen Book Data)

In this book, expansions of functions in infinite series and infinite product and the asymptotic expansion of functions are discussed. This may be the best reference book on Special Functions.
(source: Nielsen Book Data)

• Introduction-- Functions of Bounded Variation-- Approximation of Continuous Functions by Polynomials-- Functions on Metric Spaces-- Algebras of Sets and Measurable Functions-- Measure and Measurable Functions-- Integration-- Differentiation-- Appendices-- Exercises-- Bibliography-- Subject Index.
• (source: Nielsen Book Data)

This detailed and thorough introduction to classical real analysis covers both elementary and advanced material. The book also includes a number of topics not normally found in books at this level. Examples are Helly's theorems on sequences of monotone functions; Tonelli polynomials; Bernstein polynomials and absolutely monotone functions; and the theorems of Rademacher and Stepanov on differentiability of Lipschitz continuous functions. A knowledge of the elements of set theory, topology, and differential and integral calculus is required and the book also includes a large number of exercises.
(source: Nielsen Book Data)

• pt.1.The greatest integer function in the domain of the rational numbers.