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import factorial from "./factorial.js";
/** * Compute the [gamma function](https://en.wikipedia.org/wiki/Gamma_function) of a value using Nemes' approximation. * The gamma of n is equivalent to (n-1)!, but unlike the factorial function, gamma is defined for all real n except zero * and negative integers (where NaN is returned). Note, the gamma function is also well-defined for complex numbers, * though this implementation currently does not handle complex numbers as input values. * Nemes' approximation is defined [here](https://arxiv.org/abs/1003.6020) as Theorem 2.2. * Negative values use [Euler's reflection formula](https://en.wikipedia.org/wiki/Gamma_function#Properties) for computation. * * @param {number} n Any real number except for zero and negative integers. * @returns {number} The gamma of the input value. * * @example * gamma(11.5); // 11899423.084037038 * gamma(-11.5); // 2.29575810481609e-8 * gamma(5); // 24 */function gamma(n) {    if (Number.isInteger(n)) {        if (n <= 0) {            // gamma not defined for zero or negative integers            return NaN;        } else {            // use factorial for integer inputs            return factorial(n - 1);        }    }
    // Decrement n, because approximation is defined for n - 1    n--;
    if (n < 0) {        // Use Euler's reflection formula for negative inputs        // see:  https://en.wikipedia.org/wiki/Gamma_function#Properties        return Math.PI / (Math.sin(Math.PI * -n) * gamma(-n));    } else {        // Nemes' expansion approximation        const seriesCoefficient =            Math.pow(n / Math.E, n) * Math.sqrt(2 * Math.PI * (n + 1 / 6));
        const seriesDenom = n + 1 / 4;
        const seriesExpansion =            1 +            1 / 144 / Math.pow(seriesDenom, 2) -            1 / 12960 / Math.pow(seriesDenom, 3) -            257 / 207360 / Math.pow(seriesDenom, 4) -            52 / 2612736 / Math.pow(seriesDenom, 5) +            5741173 / 9405849600 / Math.pow(seriesDenom, 6) +            37529 / 18811699200 / Math.pow(seriesDenom, 7);
        return seriesCoefficient * seriesExpansion;    }}
export default gamma;