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* @license Apache-2.0
*
* Copyright (c) 2025 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.
*/
'use strict';
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var isInteger = require( '@stdlib/math/base/assert/is-integer' );
var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' );
// MAIN //
/**
* Evaluates the Chebyshev polynomial of the first kind for a degree `n` at a value `x`.
*
* @param {NonNegativeNumber} n - degree of the polynomial
* @param {number} x - input value
* @returns {number} polynomial value
*
* @example
* var y = chebyshevtpoly( 0.0, 0.5 );
* // returns 1.0
*
* @example
* var y = chebyshevtpoly( 1.0, -0.5 );
* // returns -0.5
*
* @example
* var y = chebyshevtpoly( 5.0, 0.5 );
* // returns 0.5
*
* @example
* var y = chebyshevtpoly( 2.5, 0.5 );
* // returns NaN
*
* @example
* var y = chebyshevtpoly( -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = chebyshevtpoly( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = chebyshevtpoly( 1.0, NaN );
* // returns NaN
*/
function chebyshevtpoly( n, x ) {
if (
isnan( x ) ||
!isInteger( n ) ||
n < 0.0
) {
return NaN;
}
return hyp2f1( -n, n, 0.5, 0.5*(1.0-x) );
}
// EXPORTS //
module.exports = chebyshevtpoly;
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