Math::SpecialFunctions
Raku package for mathematical special functions.
Installation
From Zef ecosytem:
zef install Math::SpecialFunctions
From GitHub:
zef install https://github.com/antononcube/Raku-Math-SpecialFunctions.git
Usage examples
The subsections below show example usage for the currently implemented functions.
Factorial
use Math::SpecialFunctions;
.say for (^11) Z=> (^11)».&factorial
# 0 => 1
# 1 => 1
# 2 => 2
# 3 => 6
# 4 => 24
# 5 => 120
# 6 => 720
# 7 => 5040
# 8 => 40320
# 9 => 362880
# 10 => 3628800
The function factorial seems reasonably fast:
my $tstart = now;
for ^1_000 { factorial($_ * (1..6).pick ) }
my $tend = now;
say "Total time {$tend - $tstart}";
say "Average time {($tend - $tstart) / 1_000}";
# Total time 0.900635487
# Average time 0.000900635487
Binomial
Pascal's triangle:
for (^6) -> $n {
say do for (0..$n) -> $k {
binomial($n, $k), " "
}.join
}
# 1
# 1 1
# 1 2 1
# 1 3 3 1
# 1 4 6 4 1
# 1 5 10 10 5 1
Bernoulli-B
For odd n, the Bernoulli numbers are equal to 0, except B[1] = -1/2.
bernoulli-b can be evaluated to arbitrary numerical precision. (Uses FatRat.)
bernoulli-b(60).nude
# (-1215233140483755572040304994079820246041491 56786730)
Gamma function
- The implementation uses approximation formula with machine numbers.
- Both function names
gamma and Γ can be used. - The property
Γ(z + 1) = z * Γ(z) holds.
Synonyms demo:
[gamma(0.3), Γ(0.3)]
# [2.991568987687589 2.991568987687589]
Show that the property above holds:
gamma(2.3) - 1.3 * gamma(1.3)
# 0
TODO