123 lines
2.7 KiB
Markdown
123 lines
2.7 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Trigamma
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> [Trigamma][trigamma-function] function.
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<section class="intro">
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The [trigamma function][trigamma-function] `ψ^(1)` is the derivative of the [digamma function][@stdlib/math/base/special/digamma].
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<!-- <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"> -->
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<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">
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<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">
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<br>
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</div>
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var trigamma = require( '@stdlib/math/base/special/trigamma' );
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```
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#### trigamma( x )
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Evaluates the [trigamma function][trigamma-function].
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```javascript
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var v = trigamma( -2.5 );
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// returns ~9.539
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v = trigamma( 1.0 );
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// returns ~1.645
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v = trigamma( 10.0 );
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// returns ~0.105
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```
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If `x` is `0` or a negative `integer`, the function returns `NaN`.
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```javascript
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var v = trigamma( 0.0 );
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// returns NaN
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v = trigamma( -1.0 );
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// returns NaN
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v = trigamma( -2.0 );
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// returns NaN
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var v = trigamma( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var trigamma = require( '@stdlib/math/base/special/trigamma' );
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var x;
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var v;
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var i;
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for ( i = 0; i < 10; i++ ) {
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x = (randu()*100.0) - 50.0;
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v = trigamma( x );
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console.log( 'x: %d, ψ^(1)(x): %d', x, v );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[trigamma-function]: https://en.wikipedia.org/wiki/Trigamma_function
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[@stdlib/math/base/special/digamma]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/digamma
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</section>
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<!-- /.links -->
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