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

• TODO Implementation

  • TODO Incomplete gamma function

  • TODO Generalized incomplete gamma function

  • TODO Digamma function

  • TODO Riemann zeta function