feat: add the JS implementation

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---

Author: anandkaranubc

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

@@ -0,0 +1,58 @@
+/**
+* @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';
+
+/**
+* Evaluate the Chebyshev polynomial of the first kind for a degree `n` at a value `x`.
+*
+* @module @stdlib/math/base/special/chebyshev-t-polynomial
+*
+* @example
+* var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' );
+*
+* var y = chebyshevtpoly( 0.0, 0.5 );
+* // returns -4.0
+*
+* y = chebyshevtpoly( 1.0, -0.5 );
+* // returns 10.0
+*
+* y = chebyshevtpoly( 5.0, 0.5 );
+* // returns 0.0
+*
+* y = chebyshevtpoly( 2.5, 0.5 );
+* // returns NaN
+*
+* y = chebyshevtpoly( -1.0, 0.5 );
+* // returns NaN
+*
+* y = chebyshevtpoly( NaN, 1.0 );
+* // returns NaN
+*
+* y = chebyshevtpoly( 1.0, NaN );
+* // returns NaN
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;

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

@@ -0,0 +1,79 @@
+/**
+* @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-x) );
+}
+
+
+// EXPORTS //
+
+module.exports = chebyshevtpoly;