Real functions related to \(\,_0F_1\)

• Bessel functions of integer order
  • Bessel function of the 1st kind, order \(0, J_{0}(x)\)
    • math53.bessel_j0()
  • Bessel function of the 1st kind, order \(1, J_{1}(x)\)
    • math53.bessel_j1()
  • Bessel function of the 1st kind, integer order \(n, J_{n}(x)\)
    • math53.bessel_jn()
  • Bessel function of the 2nd kind, order \(0, Y_{0}(x)\)
    • math53.bessel_y0()
  • Bessel function of the 2nd kind, order \(1, Y_{1}(x)\)
    • math53.bessel_y1()
  • Bessel function of the 2nd kind, integer order \(n, Y_{n}(x)\)
    • math53.bessel_yn()
  • Bessel Lambda function, \(\Lambda(\nu,x)\)
    • math53.bessel_lambda()
• Modified Bessel functions of integer order
  • Modified Bessel function of the 1st kind, order \(0, I_{0}(x)\)
    • math53.bessel_i0()
  • Modified Bessel function of the 1st kind, order \(1, I_{1}(x)\)
    • math53.bessel_i1()
  • Modified Bessel function of the 1st kind, integer order \(n, I_{n}(x)\)
    • math53.damath_bessel_in()
  • Modified Bessel function of the 2nd kind, order 0, \(K_{0}(x)\)
    • math53.bessel_k0()
  • Modified Bessel function of the 2nd kind, order \(1, K_{1}(x)\)
    • math53.bessel_k1()
  • Modified Bessel function of the 2nd kind, integer order \(n, K_{n}(x)\)
    • math53.bessel_kn()
  • Exponentially scaled modified Bessel function of the 1st kind, order \(0, I_{0,e}(x)\)
    • math53.bessel_i0e()
  • Exponentially scaled modified Bessel function of the 1st kind, order \(1, I_{1,e}(x)\)
    • math53.bessel_i1e()
  • Exponentially scaled modified Bessel function of the 2nd kind, order 0, \(K_{0,e}(x)\)
    • math53.bessel_k0e()
  • Exponentially scaled modified Bessel function of the 2nd kind, order \(1, K_{1,e}(x)\)
    • math53.bessel_k1e()
• Integrals of zero-order Bessel functions
  • Integral of \(I_0\)
    • math53.bessel_i0_int()
  • Integral of \(J_0\)
    • math53.bessel_j0_int()
  • Integral of \(K_0\)
    • math53.bessel_k0_int()
  • Integral of \(Y_0\)
    • math53.bessel_y0_int()
• Kelvin functions of order 0
  • Kelvin function \(\mathrm{ber0}(x)\)
    • math53.kelvin_ber0()
  • Kelvin function \(\mathrm{bei0}(x)\)
    • math53.kelvin_bei0()
  • Kelvin function \(\mathrm{ker0}(x)\)
    • math53.kelvin_ker0()
  • Kelvin function \(\mathrm{kei0}(x)\)
    • math53.kelvin_kei0()
  • First derivative of the Kelvin function \(\mathrm{ber0}, \mathrm{ber0}'(x)\)
    • math53.kelvin_ber0_prime()
  • First derivative of the Kelvin function \(\mathrm{bei0}, \mathrm{bei0}'(x)\)
    • math53.kelvin_bei0_prime()
  • First derivative of the Kelvin function \(\mathrm{ker0}, \mathrm{ker0}'(\nu, x)\)
    • math53.kelvin_ker0_prime()
  • First derivative of the Kelvin function \(\mathrm{kei0}, \mathrm{kei0}'(x)\)
    • math53.kelvin_kei0_prime()
• Synchrotron functions
  • First synchrotron function \(F(x)\)
    • math53.synchrotron_f()
  • Second synchrotron function \(G(x)\)
    • math53.synchrotron_g()