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<!--
@license Apache-2.0
Copyright (c) 2018 The Stdlib Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
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distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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limitations under the License.
-->
# Trigamma
> [Trigamma][trigamma-function] function.
<section class="intro">
The [trigamma function][trigamma-function] `ψ^(1)` is the derivative of the [digamma function][@stdlib/math/base/special/digamma].
<!-- <equation class="equation" label="eq:trigamma_function" align="center" raw="\psi^{(1)}(x) =\frac{d}{dx} \Psi(x) = \sum_{k=0}^\infty \frac{1}{(k+x)^2}" alt="Trigamma function"> -->
<div class="equation" align="center" data-raw-text="\psi^{(1)}(x) =\frac{d}{dx} \Psi(x) = \sum_{k=0}^\infty \frac{1}{(k+x)^2}" data-equation="eq:trigamma_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/trigamma/docs/img/equation_trigamma_function.svg" alt="Trigamma function">
<br>
</div>
<!-- </equation> -->
</section>
<!-- /.intro -->
<section class="usage">
## Usage
```javascript
var trigamma = require( '@stdlib/math/base/special/trigamma' );
```
#### trigamma( x )
Evaluates the [trigamma function][trigamma-function].
```javascript
var v = trigamma( -2.5 );
// returns ~9.539
v = trigamma( 1.0 );
// returns ~1.645
v = trigamma( 10.0 );
// returns ~0.105
```
If `x` is `0` or a negative `integer`, the function returns `NaN`.
```javascript
var v = trigamma( 0.0 );
// returns NaN
v = trigamma( -1.0 );
// returns NaN
v = trigamma( -2.0 );
// returns NaN
```
If provided `NaN`, the function returns `NaN`.
```javascript
var v = trigamma( NaN );
// returns NaN
```
</section>
<!-- /.usage -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var randu = require( '@stdlib/random/base/randu' );
var trigamma = require( '@stdlib/math/base/special/trigamma' );
var x;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
x = (randu()*100.0) - 50.0;
v = trigamma( x );
console.log( 'x: %d, ψ^(1)(x): %d', x, v );
}
```
</section>
<!-- /.examples -->
<section class="links">
[trigamma-function]: https://en.wikipedia.org/wiki/Trigamma_function
[@stdlib/math/base/special/digamma]: https://github.com/stdlib-js/math/tree/main/base/special/digamma
</section>
<!-- /.links -->
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