Compute the gamma function, the reciprocal gamma function, the logarithm of the absolute value of the gamma function, or the polygamma function. The gamma function \(\Gamma(z)\) is defined by $$\int_{0}^{\infty} t^{z - 1} e^{-t} \text{d}t$$ for \(\Re(z) > 0\) and by analytic continuation elsewhere in the \(z\)-plane, excluding poles at \(z = 0, -1, \ldots\).
arb_hypgeom_gamma(x, prec = flintPrec())
acb_hypgeom_gamma(z, prec = flintPrec())arb_hypgeom_rgamma(x, prec = flintPrec())
acb_hypgeom_rgamma(z, prec = flintPrec())
arb_hypgeom_lgamma(x, prec = flintPrec())
acb_hypgeom_lgamma(z, prec = flintPrec())
## arb_hypgeom_polygamma(s = 0, z, prec = flintPrec())
acb_hypgeom_polygamma(s = 0, z, prec = flintPrec())
An arb or acb vector
storing function values with error bounds. Its length is the maximum
of the lengths of the arguments or zero (zero if any argument has
length zero). The arguments are recycled as necessary.
numeric, complex, arb, or
acb vectors.
a numeric or slong vector indicating the
desired precision as a number of bits.
acb_hypgeom_polygamma(s, z) evaluates the polygamma function of
order s at z. The order s can be any complex
number. For nonnegative integers m, s = m corresponds
to the derivative of order m of the digamma function
\(\psi(z) = \Gamma'(z)/\Gamma(z)\). Use
acb_hypgeom_polygamma(0, z) to evaluate the digamma function at
z.
The FLINT documentation of the underlying C functions: https://flintlib.org/doc/arb_hypgeom.html, https://flintlib.org/doc/acb_hypgeom.html
NIST Digital Library of Mathematical Functions: https://dlmf.nist.gov/5
Classes arb and acb.