## NIST Handbook of Mathematical Functions Hardback and CD-ROMFrank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark 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 Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter. Check out the news release and the video for this new book! |

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### Contents

Chapter | 3 |

Algebraic and Analytic Methods | 30 |

Areas | 41 |

Numerical Methods | 72 |

Elementary Functions | 103 |

4 | 106 |

Gamma Function | 135 |

Chapter 6 | 150 |

Generalized Hypergeometric Functions | 403 |

qHypergeometric and Related Func | 419 |

R F Swarttouw | 435 |

Elliptic Integrals | 485 |

Theta Functions | 523 |

Zeta and Related Functions | 601 |

Combinatorial Analysis | 617 |

Chapter 28 | 652 |

Exponential Logarithmic Sine | 156 |

Chapter 7 | 160 |

Incomplete Gamma and Related | 173 |

Airy and Related Functions | 193 |

14 | 208 |

Bessel Functions | 215 |

Struve and Related Functions | 287 |

Parabolic Cylinder Functions | 303 |

Confluent Hypergeometric Functions | 318 |

Legendre and Related Functions | 351 |

Hypergeometric Function | 383 |

Lamé Functions | 683 |

Heun Functions | 709 |

Painlevé Transcendents | 723 |

Coulomb Functions | 741 |

3j6j9j Symbols | 757 |

Chapter 35 | 768 |

775 | |

Chapter 36 | 776 |

Integrals with Coalescing Saddles | 778 |

### Common terms and phrases

Abramowitz and Stegun Airy functions algorithm analytic analytic continuation Applications Asymptotic Approximations asymptotic expansions Bessel functions Carlson Cauchy principal value Chapter Chebyshev coefficients complex variable Computation Continued Fractions contour converges corresponding defined Definitions denote derivatives differential equation eigenvalues elliptic Erdelyi error bounds example exponential Figure finite fixed follows formula Fourier func gamma function Gautschi given Graphics hypergeometric function incomplete gamma functions infinite Integral Representations integration path interval inverse Legendre logarithmic Luke Meixner Mellin transform method NIST nonnegative integer numerically satisfactory Oberhettinger Olver orthogonal parameters pn(x points polynomials positive constant principal value Properties Prudnikov real axis Real Variable Recurrence Relations references respectively Riemann Riemann theta function sin2 singularities solutions Table tabulates Temme Theorem theta functions tions transform uniform asymptotic uniformly Watson Wong zeros