123 lines
2.6 KiB
Markdown
123 lines
2.6 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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# digamma
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> [Digamma][digamma-function] function.
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<section class="intro">
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The [digamma function][digamma-function] `ψ` is the logarithmic derivative of the [gamma function][gamma-function], i.e.
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<!-- <equation class="equation" label="eq:digamma_function" align="center" raw="\psi(x) =\frac{d}{dx} \ln{\Gamma(x)}= \frac{\Gamma\,'(x)}{\Gamma(x)}" alt="Digamma function"> -->
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<div class="equation" align="center" data-raw-text="\psi(x) =\frac{d}{dx} \ln{\Gamma(x)}= \frac{\Gamma\,'(x)}{\Gamma(x)}" data-equation="eq:digamma_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/digamma/docs/img/equation_digamma_function.svg" alt="Digamma 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 digamma = require( '@stdlib/math/base/special/digamma' );
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```
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#### digamma( x )
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Evaluates the [digamma function][digamma-function].
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```javascript
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var v = digamma( -2.5 );
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// returns ~1.103
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v = digamma( 1.0 );
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// returns ~-0.577
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v = digamma( 10.0 );
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// returns ~2.252
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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 = digamma( 0.0 );
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// returns NaN
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v = digamma( -1.0 );
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// returns NaN
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v = digamma( -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 = digamma( 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 digamma = require( '@stdlib/math/base/special/digamma' );
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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()*10.0) - 5.0;
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v = digamma( x );
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console.log( 'x: %d, f(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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[digamma-function]: https://en.wikipedia.org/wiki/Digamma_function
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[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
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</section>
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<!-- /.links -->
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