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# Tour of Special Functions

Examples and plots for Boost Special Functions

## Description

Boost library Special Functions: usage, bounds and plots

An array of Special Functions supplied by the Boost library. The library's online documentation serves as the primary reference for the following functions.

Many of the functions are only valid in certain numerical ranges. The following tour will show you plots that illustrate the behavior of the functions, their ranges and asymptotes.

## Before you get started...

Define the following functions that will lay out the plots for you:

## Gamma Functions

### Gamma, Log Gamma, Digamma, Trigamma, Polygamma

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Gamma Ratios, Incomplete/Inverses, and Derivatives of Gamma Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Beta Functions

### Beta Functions, Incomplete and Derivative

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Incomplete Beta Function Inverses

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Error Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Polynomials

### Legendre (and Associated) Polynomials

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Laguerre (and Associated) Polynomials

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Hermite Polynomials

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Chebyshev Polynomials

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Spherical Harmonics

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Bessel Functions

### Bessel and Modified Bessel Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Derivatives of Bessel and Modified Bessel Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Hankel Functions

### Cyclic Hankel Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

### Spherical Hankel Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Airy Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Elliptic Integrals

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Jacobi Elliptic Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Zeta Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Exponential Integrals

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Basic Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Sinus Cardinal (Sinc) and Hyperbolic Sinus Cardinal Functions, Inverse Hyperbolic Functions

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.

## Owen's T Function

Be sure to define ~layOutPlots and ~multiPlot at the top of the page.