confluent_hypergeometric_function_of_the_first_kind.sf

#!/usr/bin/ruby

# Simple implementation of the confluent hypergeometric function of the first kind.

# See also:
#   https://en.wikipedia.org/wiki/Confluent_hypergeometric_function
#   https://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html

func F1(a, b, z, limit=1000) {
    sum(0..limit, {|k|
        rising_factorial(a, k) / rising_factorial(b, k) * z**k / k!
    })
}

say F1(1, 1, 1)         #=> 2.71828182845904523536028747...
say F1(13, 23, 14)      #=> 6902.70292322962697731908950...
say F1(-2, 4, -3)       #=> 2.95