The Rayleigh functions are defined in terms of the zeroes of these functions. The 2-d Fourier transform of the unit disk equals two pi over the absolute value of k times one of these functions. These functions are multiplied by trigonometric exponentials in an infinite series in the Jacobi–Anger expansion. These functions result when applying the method of Frobenius to the equation "x squared y double prime plus (15[1])x y prime plus y times quantity x squared minus (*) alpha squared equals 0". Hankel functions equal a linear combination of these functions. Multivalued examples of these functions "of the second kind" are singular at the origin and are named for Neumann. A 2-D analogue of the Fourier series sums these functions of the radial coordinate, denoted J-sub-alpha of rho. For 10 points, name these functions that solve Laplace's equation in cylindrical coordinates. ■END■