feat: add JS implementation of math/base/special/legendre-polynomial

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

@@ -0,0 +1,160 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# Legendre Polynomial
+
+> Evaluate a [Legendre polynomial][legendre-polynomial].
+
+<section class="intro">
+
+The [Legendre polynomials][legendre-polynomial] $P_n(x)$ are classical orthogonal polynomials which are solutions to the Legendre differential equation
+
+<!-- <equation class="equation" label="eq:legendre_ode" align="center" raw="(1 - x^2) y'' - 2x y' + n(n+1) y = 0" alt="Legendre differential equation"> -->
+
+```math
+(1 - x^2) P_n''(x) - 2x P_n'(x) + n(n+1) P_n(x) = 0
+```
+
+<!-- <div class="equation" align="center" data-raw-text="(1 - x^2) P_n''(x) - 2x P_n'(x) + n(n+1) P_n(x) = 0" data-equation="eq:legendre_ode">
+    <img src="docs/img/equation_legendre_ode.svg" alt="Legendre differential equation">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+For **integer** non-negative $n$, they satisfy the three-term recurrence relation
+
+<!-- <equation class="equation" label="eq:legendre_recurrence" align="center" raw="(n+1) P_{n+1}(x) = (2n+1)\, x\, P_n(x) - n\, P_{n-1}(x)" alt="Legendre polynomial recurrence relation"> -->
+
+```math
+(n+1) P_{n+1}(x) = (2n+1)\, x\, P_n(x) - n\, P_{n-1}(x)
+```
+
+<!-- <div class="equation" align="center" data-raw-text="(n+1) P_{n+1}(x) = (2n+1)\, x\, P_n(x) - n\, P_{n-1}(x)" data-equation="eq:legendre_recurrence">
+    <img src="docs/img/equation_legendre_recurrence.svg" alt="Legendre polynomial recurrence relation">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+with $P_0(x) = 1$ and $P_1(x) = x$. For **non-integer** $n$, the polynomial is generalized via the relation to the Gauss hypergeometric function
+
+<!-- <equation class="equation" label="eq:legendre_hyp2f1" align="center" raw="P_n(x) = {}_2F_1 \left( -n,\, n+1;\, 1;\, \tfrac{1-x}{2} \right)" alt="Legendre polynomial via hypergeometric function"> -->
+
+```math
+P_n(x) = {}_2F_1 \left( -n,\, n+1;\, 1;\, \tfrac{1-x}{2} \right)
+```
+
+<!-- <div class="equation" align="center" data-raw-text="P_n(x) = {}_2F_1 \left( -n,\, n+1;\, 1;\, \tfrac{1-x}{2} \right)" data-equation="eq:legendre_hyp2f1">
+    <img src="docs/img/equation_legendre_hyp2f1.svg" alt="Legendre polynomial via hypergeometric function">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' );
+```
+
+#### legendrepoly( n, x )
+
+Evaluates a [Legendre polynomial][legendre-polynomial] of degree `n` at a point `x`.
+
+```javascript
+var v = legendrepoly( 1.0, 0.5 );
+// returns 0.5
+
+v = legendrepoly( 2.0, 0.5 );
+// returns -0.125
+```
+
+If `n` is not an integer, the polynomial is evaluated using the Gauss hypergeometric function.
+
+```javascript
+var v = legendrepoly( 1.5, 0.5 );
+// returns ~0.172
+```
+
+If provided `NaN` for any argument, the function returns `NaN`.
+
+```javascript
+var v = legendrepoly( NaN, 0.5 );
+// returns NaN
+
+v = legendrepoly( 1.0, NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/base/uniform' );
+var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' );
+
+var x;
+var n;
+var v;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+    n = uniform( -50.0, 50.0 );
+    x = uniform( -1.0, 1.0 );
+    v = legendrepoly( n, x );
+    console.log( 'P_%d(%d) = %d', n, x, v );
+}
+```
+
+</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">
+
+[legendre-polynomial]: https://en.wikipedia.org/wiki/Legendre_polynomials
+
+</section>
+
+<!-- /.links -->

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

@@ -0,0 +1,54 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var legendrepoly = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var n;
+	var x;
+	var y;
+	var i;
+
+	n = uniform( 100, -50.0, 50.0 );
+	x = uniform( 100, -1.0, 1.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = legendrepoly( 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/legendre-polynomial/docs/types/index.d.ts

@@ -0,0 +1,45 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 a Legendre polynomial.
+*
+* @param n - degree of the polynomial
+* @param x - evaluation point
+* @returns polynomial value
+*
+* @example
+* var v = legendrepoly( 1.0, 0.5 );
+* // returns 0.5
+*
+* @example
+* var v = legendrepoly( 2.0, 0.5 );
+* // returns -0.125
+*
+* @example
+* var v = legendrepoly( 1.5, 0.5 );
+* // returns ~0.172
+*/
+declare function legendrepoly( n: number, x: number ): number;
+
+
+// EXPORTS //
+
+export = legendrepoly;

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

@@ -0,0 +1,52 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 legendrepoly = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	legendrepoly( 1.0, 0.5 ); // $ExpectType number
+	legendrepoly( 2.0, 0.5 ); // $ExpectType number
+	legendrepoly( 1.5, 0.5 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided values other than two numbers...
+{
+	legendrepoly( true, 0.5 ); // $ExpectError
+	legendrepoly( false, 0.5 ); // $ExpectError
+	legendrepoly( '5', 0.5 ); // $ExpectError
+	legendrepoly( [], 0.5 ); // $ExpectError
+	legendrepoly( {}, 0.5 ); // $ExpectError
+	legendrepoly( ( x: number ): number => x, 0.5 ); // $ExpectError
+
+	legendrepoly( 1.0, true ); // $ExpectError
+	legendrepoly( 1.0, false ); // $ExpectError
+	legendrepoly( 1.0, '5' ); // $ExpectError
+	legendrepoly( 1.0, [] ); // $ExpectError
+	legendrepoly( 1.0, {} ); // $ExpectError
+	legendrepoly( 1.0, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	legendrepoly(); // $ExpectError
+	legendrepoly( 1.0 ); // $ExpectError
+}

lib/node_modules/@stdlib/math/base/special/legendre-polynomial/examples/index.js

@@ -0,0 +1,34 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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';
+
+var uniform = require( '@stdlib/random/base/uniform' );
+var legendrepoly = require( './../lib' );
+
+var x;
+var n;
+var v;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+	n = uniform( -50.0, 50.0 );
+	x = uniform( -1.0, 1.0 );
+	v = legendrepoly( n, x );
+	console.log( 'P_%d(%d) = %d', n, x, v );
+}

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

@@ -0,0 +1,46 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 a Legendre polynomial.
+*
+* @module @stdlib/math/base/special/legendre-polynomial
+*
+* @example
+* var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' );
+*
+* var v = legendrepoly( 1.0, 0.5 );
+* // returns 0.5
+*
+* v = legendrepoly( 0.0, 0.5 );
+* // returns 1.0
+*
+* v = legendrepoly( 2.0, 0.5 );
+* // returns -0.125
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;