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version 2.112.0

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Function std.mathspecial.digamma

Digamma function, Ψ(x)

real digamma(
  real x
) pure nothrow @nogc @safe;

Ψ(x), is the logarithmic derivative of the gamma function, Γ(x).

Ψ(x) = d/dx ln|Γ(x)| (the derivative of logGamma(x))

Parameters

NameDescription
x the domain value

Returns

It returns Ψ(x).

Special Values
x digamma(x)
integer < 0 NAN
±0.0 ∓∞
+∞ +∞
-∞ NAN
NAN NAN

See Also

logmdigamma, logmdigammaInverse.

Example

const euler = 0.57721_56649_01532_86060_65121L;

assert(isClose(digamma(1), -euler));
writeln(digamma(+0.)); // -real.infinity
writeln(digamma(-0.)); // +real.infinity
writeln(digamma(+real.infinity)); // +real.infinity
assert(isNaN(digamma(-1)));
assert(isNaN(digamma(-real.infinity)));

Authors

Stephen L. Moshier (original C code). Conversion to D by Don Clugston

License

Boost License 1.0.