MathPHP\Functions\Map\Single::add PHP Method

    public static function add(array $xs, $k) : array
    {
        return array_map(function ($x) use($k) {
            return $x + $k;
        }, $xs);
    }

 /**
  * Generalized Hypergeometric Function
  *
  * https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
  *
  *                                       ∞
  *                                      ____
  *                                      \     ∏ap⁽ⁿ⁾ * zⁿ
  * pFq(a₁,a₂,...ap;b₁,b₂,...,bq;z)=      >    ------------
  *                                      /      ∏bq⁽ⁿ⁾ * n!
  *                                      ‾‾‾‾
  *                                       n=0
  *
  * Where a⁽ⁿ⁾ is the Pochhammer Function or Rising Factorial
  *
  * We are evaluating this as a series:
  *
  *               (a + n - 1) * z
  * ∏n = ∏n₋₁  * -----------------
  *               (b + n - 1) * n
  *
  *                  n   (a + n - 1) * z
  *   ₁F₁ = ₁F₁n₋₁ + ∏  -----------------  = ₁F₁n₋₁ + ∏n
  *                  1   (b + n - 1) * n
  *
  * @param int   $p      the number of parameters in the numerator
  * @param int   $q      the number of parameters in the denominator
  * @param array $params a collection of the a, b, and z parameters
  *
  * @return number
  *
  * @throws BadParameterException if the number of parameters is incorrect
  */
 public static function generalizedHypergeometric(int $p, int $q, ...$params)
 {
     $n = count($params);
     if ($n !== $p + $q + 1) {
         $expected_num_params = $p + $q + 1;
         throw new Exception\BadParameterException("Number of parameters is incorrect. Expected {$expected_num_params}; got {$n}");
     }
     $a = array_slice($params, 0, $p);
     $b = array_slice($params, $p, $q);
     $z = $params[$n - 1];
     $tol = 1.0E-8;
     $n = 1;
     $sum = 0;
     $product = 1;
     do {
         $sum += $product;
         $a_sum = array_product(Single::add($a, $n - 1));
         $b_sum = array_product(Single::add($b, $n - 1));
         $product *= $a_sum * $z / $b_sum / $n;
         $n++;
     } while ($product / $sum > $tol);
     return $sum;
 }