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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
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_53_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html}. The implementation follows the original but has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var ln = require( '@stdlib/math/base/special/ln' );
var polyval = require( './polyval_p.js' );
// MAIN //
/**
* Evaluates the digamma function via asymptotic expansion.
*
* @private
* @param {number} x - input value
* @returns {number} function value
*/
function digamma( x ) {
var y;
var z;
x -= 1.0;
y = ln(x) + ( 1.0 / (2.0*x) );
z = 1.0 / (x*x);
return y - ( z*polyval( z ) );
}
// EXPORTS //
module.exports = digamma;
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