NevilleThetaC[z, m] gives the Neville theta function \[CurlyTheta]_c (z \[VerticalSeparator] m).
InverseJacobiCD[v, m] gives the inverse Jacobi elliptic function cd -1 (v \[VerticalSeparator] m).
InverseJacobiCS[v, m] gives the inverse Jacobi elliptic function cs -1 (v \[VerticalSeparator] m).
InverseJacobiDN[v, m] gives the inverse Jacobi elliptic function dn -1 (v \[VerticalSeparator] m).
InverseJacobiDS[v, m] gives the inverse Jacobi elliptic function ds -1 (v \[VerticalSeparator] m).
InverseJacobiND[v, m] gives the inverse Jacobi elliptic function nd -1 (v \[VerticalSeparator] m).
InverseJacobiSC[v, m] gives the inverse Jacobi elliptic function sc -1 (v \[VerticalSeparator] m).
InverseJacobiSD[v, m] gives the inverse Jacobi elliptic function sd -1 (v \[VerticalSeparator] m).
InverseErfc[s] gives the inverse complementary error function obtained as the solution for z in s = erfc(z).
Nested logical and piecewise functions can be expanded out much like nested arithmetic functions. You can do this using LogicalExpand and PiecewiseExpand. Expanding out ...