Ramanujan's constant: Difference between revisions

J natively supports arithmetic types Boolean 0 1, integer 00 01 2 3 9, extended integer<ref>Taking a rational power of an extended integer produces a floating-point result whenever the denominator of the power is not 1.</ref> 9x, rational 1r2, floating point as c double, and complex numbers 2ad90 (radius 2, 90 angle in degrees). J does not natively support arbitrary precision decimal, or ternary. J can format a rationalsrational as arbitrary precision base 10 literals.

Rational arithmetic with series expansion therefor serves to compute Ramanujan's constant. We test for convergence in the base 10 literal expression over the required length. Exponential expansion of "long" rational numbers and the number of terms needed for "large" numbers is unwieldly. We divide by 8x, then raise the series sum to the 8th power. We also convert the rational exponent to a base 10 rational number of sufficient digits to reduce size. Tolerant continued fraction expansion reduces the magnitude of the exponent's numerator and denominator.