Sometimes you may want to set up functions where certain arguments, if omitted, are given "default values". The pattern x_:v stands for an object that can be omitted, and if ...

For ordinary polynomials, Factor and Expand give the most important forms. For rational expressions, there are many different forms that can be useful. Different kinds of ...

Mathematica does operations like numerical integration very differently from the way it does their symbolic counterparts. When you do a symbolic integral, Mathematica takes ...

This section is designed to discuss how to make compiled functions run efficiently. It will cover features that make them run faster, as well as problems that can make them ...

DegreeCentrality[g] gives a list of vertex degrees for the vertices in the underlying simple graph of g. DegreeCentrality[g, "InDegree"] gives a list of vertex ...

QPochhammer[a, q, n] gives the q-Pochhammer symbol (a; q) n.QPochhammer[a, q] gives the q-Pochhammer symbol (a; q) \[Infinity].QPochhammer[q] gives the q-Pochhammer symbol ...

ThreeJSymbol[{j_1, m_1}, {j_2, m_2}, {j_3, m_3}] gives the values of the Wigner 3-j symbol.

VertexOutDegree[g] gives the list of vertex out-degrees for all vertices in the graph g.VertexOutDegree[g, v] gives the vertex out-degree for the vertex v.

WaveletPhi[wave, x] gives the scaling function \[Phi](x) for the symbolic wavelet wave evaluated at x.WaveletPhi[wave] gives the scaling function as a pure function.

ExpIntegralE[n, z] gives the exponential integral function E_n (z).