Analytic Number Theory (Mathematica Guide)

Building on its broad strengths in mathematics in general, and in special functions in particular, Mathematica provides a unique level of support for analytic number theory, ...

LogBarnesG (Built-in Mathematica Symbol)

LogBarnesG[z] gives the logarithm of the Barnes G-function logG(z).

WeierstrassZeta (Built-in Mathematica Symbol)

WeierstrassZeta[u, {g_2, g_3}] gives the Weierstrass zeta function \[Zeta](u; g_2, g_3).

HurwitzZeta (Built-in Mathematica Symbol)

HurwitzZeta[s, a] gives the Hurwitz zeta function \[Zeta](s, a).

WhittakerW (Built-in Mathematica Symbol)

WhittakerW[k, m, z] gives the Whittaker function W k, m (z).

Gamma (Built-in Mathematica Symbol)

Gamma[z] is the Euler gamma function \[CapitalGamma](z). Gamma[a, z] is the incomplete gamma function \[CapitalGamma](a, z). Gamma[a, z_0, z_1] is the generalized incomplete ...

StruveL (Built-in Mathematica Symbol)

StruveL[n, z] gives the modified Struve function L n (z).

WeierstrassSigma (Built-in Mathematica Symbol)

WeierstrassSigma[u, {g_2, g_3}] gives the Weierstrass sigma function \[Sigma](u; g_2, g_3).

ExponentialGeneratingFunction (Built-in Mathematica Symbol)

ExponentialGeneratingFunction[expr, n, x] gives the exponential generating function in x for the sequence whose n\[Null]^th term is given by the expression ...

Diophantine Equations (Mathematica Guide)

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...