Published by David and Gregory Chudnovsky in 1988. Still the workhorse behind serious digit hunts. Each term is expensive. Each term is also efficiently delicious.
Key ingredients
kThe term index. Start at 0. Keep going until the digits stop changing in the window you care about.(6k)!, (3k)!, k!Factorials that swell immediately. In the kitchen you update ratios from the last term, or binary-split the whole sum.13591409, 545140134Constants in the formula, arising from the mathematical derivation of the series.6403203k + 3/2That half-power is why implementations often rewrite the constant as 426880 √10005.12The prefactor that turns the sum into 1/π.
Use in Computing π
The Chudnovsky algorithm is widely used in programs for computing millions or even trillions of digits of π/pi, leveraging its rapid convergence and ability to compute terms in parallel.
In the Kitchen
In practice the algorithm is implemented with optimizations for factorial computations and large integer arithmetic to handle the immense size of the numbers involved in calculations.
Enjoy a Sample
Your Slice is the tasting spoon — a browser bake, once the house calculations are dropped in. For a bound copy, see the books.