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

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

Published $\text {1968}$.

Previous  ... Next

## $16 \quad$ 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

Previous  ... Next