LogGamma[z] gives the logarithm of the gamma function log \[CapitalGamma](z).
NevilleThetaN[z, m] gives the Neville theta function \[CurlyTheta]_n (z \[VerticalSeparator] m).
NevilleThetaS[z, m] gives the Neville theta function \[CurlyTheta]_s (z \[VerticalSeparator] m).
Rationalize[x] converts an approximate number x to a nearby rational with small denominator. Rationalize[x, dx] yields the rational number with smallest denominator that lies ...
SinIntegral[z] gives the sine integral function Si(z).
SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.
WorkingPrecision is an option for various numerical operations that specifies how many digits of precision should be maintained in internal computations.
ArcCos
(Built-in Mathematica Symbol) ArcCos[z] gives the arc cosine cos -1 (z) of the complex number z.
DirichletCharacter[k, j, n] gives the Dirichlet character \[Chi] {k, j} (n) with modulus k and index j.
Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...