Real functions related to Lerchs phi

• Polygamma, and related functions
  • Pentagamma function \(\psi'''(x)\)
    • math53.pentagamma()
  • Tetragamma function, \(\psi''(x)\)
    • math53.tetragamma()
  • Auxiliary function \(\psi^{*}(x)\)
    • math53.psistar()
  • Inverse digamma function \(\psi^{-1}(y)\)
    • math53.psi_inv()
  • Bateman function \(G(x)\)
    • math53.bateman_g()
• Polylogarithm, and related functions
  • Polylogarithm of integer order, \(\mathrm{Li}_n(x)\)
    • math53.polylog_i()
  • Fermi-Dirac integrals of integer order, \(F_n(x)\)
    • math53.fermi_dirac_i()
  • Fermi-Dirac integral \(F_{-1/2}(x)\)
    • math53.fermi_dirac_m05()
  • Fermi-Dirac integral \(F_{1/2}(x)\)
    • math53.fermi_dirac_p05()
  • Fermi-Dirac integral \(F_{3/2}(x)\)
    • math53.fermi_dirac_p15()
  • Fermi-Dirac integral \(F_{5/2}(x)\)
    • math53.fermi_dirac_p25()
  • Inverse tangent integral, \(\mathrm{Ti}_2(x)\)
    • math53.tangent_int_2()
  • Lobachevsky’s log-cos integral, \(L(x)\)
    • math53.lobachevsky_c()
  • Lobachevsky’s log-sin integral, \(\Lambda(x)\)
    • math53.lobachevsky_s()
  • Debye functions, \(\mathrm{D}_n(x)\)
    • math53.debye()
  • Transport integral, \(\mathrm{J}_n(x)\)
    • math53.transport_jn()
• Riemann zeta, and related functions
  • Riemann \(\zeta(n)\) for integer arguments
    • math53.zeta_i()
  • Riemann \(\zeta(1+x)\)
    • math53.zeta1p()
  • Dirichlet eta function for integer argument, \(\eta(n)\)
    • math53.dirichlet_eta_i()
  • Prime zeta function
    • math53.prime_zeta()
  • Riemann prime counting function, \(R(x)\)
    • math53.riemann_r()
  • Inverse of the Riemann prime counting function, \(R^{-1}(x)\)
    • math53.riemann_r_inv()
  • Rogers-Ramanujan continued fraction
    • math53.rogers_ramanujan_cf()
  • Moebius function, \(\mu(n)\)
    • math53.moebius()
  • q-Pochhammer Euler function, \((q)_{\infty}\)
    • math53.euler_q()
• Miscellaneous functions
  • Log-series distribution, pmf
    • math53.logseries_pmf()
  • Log-series distribution, cdf
    • math53.logseries_cdf()
  • Zeta distribution, pmf
    • math53.zeta_pmf()
  • Zeta distribution, cdf
    • math53.zeta_cdf()