Book description

The numerous applications of special functions in solving many of the more difficult problems in physics, engineering, and mathematics make their development a continuous and evolving process. Bringing new insight to these functions, the Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas presents new results and includes some known functions for completeness in coverage. This collection of functions contains— Differentiation formulas for various functions

• Limit formula for the special functions that depend on parameters
• Formulas of integration and summation for elementary and special
• functions, new class integrals, finite sums, and infinite series being considered
• Connection formulas for various elementary and special functions
• Representatives of hydrogeometrics functions and Meijer G functions in terms of other functions for various values of parameters and arguments
• Representations of a variety of elementary and special functions in terms of hypergeometric functions

The author pays special attention to formulas of derivatives of nth order with respect to the argument and of the first derivatives with respect to the parameters of most elementary and special functions. A majority of the book is devoted to formulas of connection and conversion for elementary and special functions, especially for hypergeometric and Meijer G functions, and it concludes with a list of standard notations. The handbook provides the tools necessary for solving the diversity of problems whose solutions require knowledge of elementary and special functions of mathematics.

Table of contents