ParabolicCylinderD[\[Nu], z] gives the parabolic cylinder function D_\[Nu] (z).
Subfactorial[n] gives the number of permutations of n objects that leave no object fixed.
ZernikeR[n, m, r] gives the radial Zernike polynomial R_n^m(r).
JacobiP
(Built-in Mathematica Symbol) JacobiP[n, a, b, x] gives the Jacobi polynomial P_n^(a, b)(x).
NevilleThetaC[z, m] gives the Neville theta function \[CurlyTheta]_c (z \[VerticalSeparator] m).
WeierstrassZeta[u, {g_2, g_3}] gives the Weierstrass zeta function \[Zeta](u; g_2, g_3).
"Introduction to Manipulate" and "Introduction to Dynamic" provide most of the information you need to use Mathematica's interactive features accessible through the functions ...
f' represents the derivative of a function f of one argument. Derivative[n_1, n_2, ...][f] is the general form, representing a function obtained from f by differentiating n_1 ...
AppellF1[a, b_1, b_2, c, x, y] is the Appell hypergeometric function of two variables F_1 (a; b_1, b_2; c; x, y).
HypergeometricU[a, b, z] is the confluent hypergeometric function U(a, b, z).