# airyBi

Airy function of the second kind

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```airyBi(`z`)
airyBi(`z`, `n`)
```

## Description

`airyBi(z)` represents the Airy function of the second kind. The Airy functions `airyAi(z)` and `airyBi(z)` are linearly independent solutions of the differential equation .

The call `airyBi(z)` is equivalent to ```airyBi(z, 0)```.

`airyBi(z, n)` represents the n-th derivative of `airyBi(z)` with respect to z.

For n ≥ 2, derivatives of the Airy functions are automatically expressed in terms of the Airy functions and their first derivative. See Example 1.

`airyBi` returns special values for z = 0 and . For all other symbolic values of z, unevaluated function calls are returned. See Example 2.

## Environment Interactions

When called with floating-point arguments, this functions is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

Second and higher derivatives of Airy functions are rewritten in terms of Airy functions and their first derivatives:

`airyAi(x), airyAi(x, 1), airyBi(sin(x), 3)`

### Example 2

For z = 0, special values are returned:

`airyAi(0), airyBi(0, 1), airyAi(0, 27)`

For n = 0, 1 and any symbolic , a symbolic call is returned:

`airyAi(-1), airyBi(x, 1)`

floating-point values are returned for floating-point arguments:

`airyBi(0.0), airyAi(-3.24819, 1), airyBi(-3.45 + 2.75*I);`

### Example 3

The functions `diff`, `float`, `limit`, and `series` handle expressions involving the Airy functions

`diff(airyBi(x^2), x), float(airyAi(PI))`

```limit(airyAi(-x), x = infinity), series(airyBi(x, 1), x = infinity, 4)```

## Parameters

 `z` Arithmetical expression `n` Arithmetical expression representing a nonnegative integer

## Return Values

Arithmetical expression.

`z`

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