ExpIntegralE[n, z] gives the exponential integral function E_n (z).
LerchPhi[z, s, a] gives the Lerch transcendent \[CapitalPhi] (z, s, a).
When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...
Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...
ArcCos
(Built-in Mathematica Symbol) ArcCos[z] gives the arc cosine cos -1 (z) of the complex number z.
Cosh
(Built-in Mathematica Symbol) Cosh[z] gives the hyperbolic cosine of z.
Coth
(Built-in Mathematica Symbol) Coth[z] gives the hyperbolic cotangent of z.
Cot
(Built-in Mathematica Symbol) Cot[z] gives the cotangent of z.
Csch
(Built-in Mathematica Symbol) Csch[z] gives the hyperbolic cosecant of z.
EllipticTheta[a, u, q] gives the theta function \[CurlyTheta]_a (u, q) (a = 1, ..., 4).