Real and complex functions

• Additional elementary complex functions
  • Auxiliary function \(\sqrt{1-z^2}\)
    • math53.sqrt1mz2()
  • Cube root, \(\mathrm{cuberoot}(x) = \sqrt[3]{x} = y\), with \(\mathrm{arg}(y)\) closest to \(\mathrm{arg}(x)\)
    • math53.cuberoot()
  • Nth root, \(\mathrm{surd}(x, n) = \sqrt[n]{x} = y\), with \(\mathrm{arg}(y)\) closest to \(\mathrm{arg}(x)\)
    • mathc53.surd()
  • Continuous inverse cotangent, \(\mathrm{acotc}(x)\)
    • ctx.acotc()
  • Continuous inverse hyperbolic cotangent, \(\mathrm{acothc}(x)\)
    • ctx.acothc()
• Neville theta functions
  • Neville \(\theta_s(x,k)\)
    • math53.neville_theta_s()
  • Neville \(\theta_c(x,k)\)
    • math53.neville_theta_c()
  • Neville \(\theta_d(x,k)\)
    • math53.neville_theta_d()
  • Neville \(\theta_n(x,k)\)
    • math53.neville_theta_n()
• Conversions of parameters of Weierstrass \(\wp\)
  • Elliptic lattice roots \(e_1, e_2, e_3\) from elliptic lattice invariants \(g_2, g_3\)
    • ctx.elliptic_roots_from_g2g3()
  • Elliptic half periods \(\omega_1, \omega_2\) from elliptic lattice invariants \(g_2, g_3\)
    • ctx.elliptic_halfperiods_from_g2g3()
  • Elliptic half-period \(\omega_1\) and elliptic period ratio \(\tau\) from elliptic lattice invariants \(g_2\) and \(g_3\)
    • ctx.omega_and_tau_from_g2g3()
• Weierstrass elliptic functions, in terms of (real) lattice invariants \(g_2, g_3\)
  • Weierstrass function \(\wp_g(z, g_2, g_3)\) (also DAMath)
    • ctx.weierstrass_p_g()
  • Weierstrass function, first derivative: \(\wp_g'(z, g_2, g_3)\)
    • ctx.weierstrass_p_prime_()
  • Inverse Weierstrass function \(\wp_g^{-1}(z, g_2, g_3)\)
    • ctx.weierstrass_p_invG()
  • Weierstrass Zeta function \(\zeta_g(z, g_2, g_3)\)
    • ctx.weierstrass_zeta_g()
  • Weierstrass Sigma function \(\sigma_g(z, g_2, g_3\))
    • ctx.weierstrass_sigma_g()
• Weierstrass elliptic functions, in terms of (real) lattice roots \(e_1, e_2\)
  • Weierstrass function \(\wp_e(x,e_1,e_2)\) (also DAMath)
    • ctx.weierstrass_p_e()
  • Weierstrass function \(\wp'_e(x,e_1,e_2)\) (also DAMath)
    • ctx.weierstrass_pprime_e()
  • Inverse Weierstrass function \(\wp^{-1}_e(y,e_1,e_2)\) (also DAMath)
    • ctx.weierstrass_p_inv_e()
  • Weierstrass Zeta function \(\zeta_e(z, e_1, e_2)\)
    • ctx.weierstrass_zeta_e()
  • Weierstrass Sigma function \(\sigma_e(z, e_1, e_2)\)
    • ctx.weierstrass_sigma_e()
• Weierstrass elliptic functions, in terms of lattice half-periods \(\omega_1\) and \(\omega_2\)
  • Weierstrass function \(\wp_{\omega}(z| \omega_1, \omega_2)\)
    • ctx.weierstrass_o()
  • Weierstrass function, first derivative: \(\wp_{\omega}'(z| \omega_1, \omega_2)\)
    • ctx.weierstrass_p_prime_o()
  • Inverse Weierstrass function \(\wp_{\omega}^{-1}(z| \omega_1, \omega_2)\)
    • ctx.weierstrass_p_inv_o()
  • Weierstrass Zeta function \(\zeta_{\omega}(z, \omega_1, \omega_2)\)
    • ctx.weierstrass_zeta_o()
  • Weierstrass Sigma function \(\sigma_{\omega}(z| \omega_1, \omega_2)\)
    • ctx.weierstrass_sigma_o()