  Kummer's function, also known as the confluent hypergeometric function (CHF),
is an important mathematical function, in particular due to its many special
cases, which include the Bessel function, the incomplete Gamma function and the
error function (erf). The CHF has no closed form expression, but instead is
most commonly expressed as an infinite sum of ratios of rising factorials,
which makes its precise and efficient calculation challenging. It is a function
of three parameters, the first two being the rising factorial base of the
numerator and denominator, and the third being a scale parameter. Accurate and
efficient calculation for large values of the scale parameter is particularly
challenging due to numeric underflow and overflow which easily occur when
summing the underlying component terms. This work presents an elegant and
precise mathematical algorithm for the calculation of the CHF, which is of
particular advantage for large values of the scale parameter. This method
massively reduces the number and range of component terms which need to be
summed to achieve any required precision, thus obviating the need for the
computationally intensive transformations needed by current algorithms.
