Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 16

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 16

Published $\text {1968}$

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$16 \quad$ The Gamma Function

Definition of the Gamma Function $\map \Gamma n$ for $n > 0$

$16.1$: Gamma Function: Integral Form

Recursion Formula

$16.2$: Gamma Difference Equation

$16.3$: Gamma Function Extends Factorial

The Gamma Function for $n < 0$

$16.4$: Gamma Function for Non-Negative Integer Argument

Graph of the Gamma Function

Gamma Function: Graph

Special Values of the Gamma Function

$16.5$: Gamma Function of One Half

$16.6$: Gamma Function of Positive Half-Integer

$16.7$: Gamma Function of Negative Half-Integer

Relationships among Gamma Functions

$16.8$: Euler's Reflection Formula

$16.9$: Legendre's Duplication Formula

$16.10$: Gauss Multiplication Formula

Other Definitions of the Gamma Function

$16.11$: Gamma Function: Euler Form

$16.12$: Gamma Function: Weierstrass Form

Derivatives of the Gamma Function

$16.13$: Derivative of Gamma Function at $1$

$16.14$: Reciprocal times Derivative of Gamma Function

Asymptotic Expansions for the Gamma Function

$16.15$: Stirling's Formula for Gamma Function

$16.16$: Stirling's Formula

Miscellaneous

$16.17$: Modulus of Gamma Function of Imaginary Number

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