feat: add math/base/special/chebyshev-t-polynomial

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

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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.
+
+-->
+
+# chebyshevtpoly
+
+> [Chebyshev Polynomial][chebyshev-polynomial] of the first kind.
+
+<section class="intro">
+
+The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is defined as
+
+<!-- <equation class="equation" label="eq:chebyshev_polynomial" align="center" raw="T_n(x) = \cos( n \cos^{-1}(x) )" alt="Chebyshev Polynomial of the first kind."> -->
+
+```math
+T_n(x) = \cos( n \cos^{-1}(x) )
+```
+
+<!-- </equation> -->
+
+where `n` is the polynomial degree.
+
+The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is related to the Gaussian hypergeometric function via the following equation
+
+<!-- <equation class="equation" label="eq:chebyshev_polynomial2" align="center" raw="T_n(x) = {}_2F_1\left( -n, n; \frac{1}{2}; \frac{1}{2}(1-x) \right)" alt="Chebyshev Polynomial of the first kind expressed in terms of the Gaussian hypergeometric function."> -->
+
+```math
+T_n(x) = {}_2F_1\left( -n, n; \frac{1}{2}; \frac{1}{2}(1-x) \right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' );
+```
+
+#### chebyshevtpoly( n, x )
+
+Evaluates the [Chebyshev Polynomial][chebyshev-polynomial] of the first kind for a degree `n` at a value `x`.
+
+```javascript
+var y = chebyshevtpoly( 0.0, 0.5 );
+// returns 1.0
+
+y = chebyshevtpoly( 1.0, -0.5 );
+// returns -0.5
+
+y = chebyshevtpoly( 5.0, 0.5 );
+// returns 0.5
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = chebyshevtpoly( NaN, 1.0 );
+// returns NaN
+
+y = chebyshevtpoly( 0.0, NaN );
+// returns NaN
+```
+
+If provided a polynomial degree `n < 0`, the function returns `NaN`.
+
+```javascript
+var y = chebyshevtpoly( -2.0, 0.5 );
+// returns NaN
+
+y = chebyshevtpoly( -4.5, -0.5 );
+// returns NaN
+```
+
+If provided a polynomial degree `n` which is not a nonnegative integer, the function returns `NaN`.
+
+```javascript
+var y = chebyshevtpoly( 2.5, 0.5 );
+// returns NaN
+
+y = chebyshevtpoly( 0.5, -0.5 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' );
+
+var n;
+var x;
+var y;
+var i;
+
+for ( i = 0; i < 10; i++ ) {
+    n = round( randu()*10.0 );
+    x = ( randu()*2.0 ) - 1.0;
+    y = chebyshevtpoly( n, x );
+    console.log( 'n: %d, x: %d, T_n(x): %d', n.toFixed( 4 ), x.toFixed( 4 ), y.toFixed( 4 ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[chebyshev-polynomial]: https://en.wikipedia.org/wiki/Chebyshev_polynomials#Definitions
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/benchmark/benchmark.js

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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 bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var chebyshevtpoly = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var n;
+	var x;
+	var y;
+	var i;
+
+	n = discreteUniform( 100, 0, 50 );
+	x = uniform( 100, -1.0, 1.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = chebyshevtpoly( n[ i % n.length ], x[ i % x.length ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/repl.txt

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+
+{{alias}}( n, x )
+    Evaluates the Chebyshev polynomial of the first kind
+    for a degree `n` at a value `x`.
+
+    Parameters
+    ----------
+    n: number
+        Degree of the polynomial.
+
+    x: number
+        Input value.
+
+    Returns
+    -------
+    out: number
+        Polynomial value.
+
+    Examples
+    --------
+    > var y = {{alias}}( 0.0, 0.5 )
+    1.0
+    > y = {{alias}}( 1.0, -0.5 )
+    -0.5
+    > y = {{alias}}( 5.0, 0.5 )
+    0.5
+    > y = {{alias}}( 2.5, 0.5 )
+    NaN
+    > y = {{alias}}( -1.0, 0.5 )
+    NaN
+    > y = {{alias}}( NaN, 1.0 )
+    NaN
+    > y = {{alias}}( 1.0, NaN )
+    NaN
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/index.d.ts

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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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Evaluates the Chebyshev polynomial of the first kind for a degree `n` at a value `x`.
+*
+* @param n - degree of the polynomial
+* @param x - input value
+* @returns 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
+*/
+declare function chebyshevtpoly( n: number, x: number ): number;
+
+
+// EXPORTS //
+
+export = chebyshevtpoly;

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/test.ts

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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.
+*/
+
+import chebyshevtpoly = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	chebyshevtpoly( 8.0, 1.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided values other than two numbers...
+{
+	chebyshevtpoly( true, 3 ); // $ExpectError
+	chebyshevtpoly( false, 2 ); // $ExpectError
+	chebyshevtpoly( '5', 1 ); // $ExpectError
+	chebyshevtpoly( [], 1 ); // $ExpectError
+	chebyshevtpoly( {}, 2 ); // $ExpectError
+	chebyshevtpoly( ( x: number ): number => x, 2 ); // $ExpectError
+
+	chebyshevtpoly( 9, true ); // $ExpectError
+	chebyshevtpoly( 9, false ); // $ExpectError
+	chebyshevtpoly( 5, '5' ); // $ExpectError
+	chebyshevtpoly( 8, [] ); // $ExpectError
+	chebyshevtpoly( 9, {} ); // $ExpectError
+	chebyshevtpoly( 8, ( x: number ): number => x ); // $ExpectError
+
+	chebyshevtpoly( [], true ); // $ExpectError
+	chebyshevtpoly( {}, false ); // $ExpectError
+	chebyshevtpoly( false, '5' ); // $ExpectError
+	chebyshevtpoly( {}, [] ); // $ExpectError
+	chebyshevtpoly( '5', ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	chebyshevtpoly(); // $ExpectError
+	chebyshevtpoly( 3 ); // $ExpectError
+}