SSRN Author: Christopher Paul NofalChristopher Paul Nofal SSRN Content
http://www.ssrn.com/author=1639750
http://www.ssrn.com/rss/en-usWed, 20 Sep 2017 02:40:24 GMTeditor@ssrn.com (Editor)Wed, 20 Sep 2017 02:40:24 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0New: Proof of Bessel's Relation: Part IBessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates. Bessel functions are therefore especially important for many problems of wave propagation and static potentials. In solving problems in cylindrical coordinate systems, one obtains Bessel functions of integer order (v = n); in spherical problems, one obtains half-integer orders (v = n ± ½). This paper claims that a Bessel function of higher order can be expressed by Bessel functions of lower orders.
http://www.ssrn.com/abstract=3035454
http://www.ssrn.com/1626743.htmlTue, 19 Sep 2017 18:46:11 GMTNew: Proof of Bessel's Relation: Part IIBessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates. Bessel functions are therefore especially important for many problems of wave propagation and static potentials. In solving problems in cylindrical coordinate systems, one obtains Bessel functions of integer order (v = n); in spherical problems, one obtains half-integer orders (v = n ± ½). This paper claims that a Bessel function of higher order can be expressed by Bessel functions of lower orders.
http://www.ssrn.com/abstract=3037673
http://www.ssrn.com/1626700.htmlTue, 19 Sep 2017 14:33:34 GMTNew: Proof that the Natural Logarithm Can Be Represented by the Gaussian Hypergeometric FunctionThe Gaussian or ordinary hypergeometric function is a special function represented by the hypergeometric series that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE). Every second-order linear ODE with three regular singular points can be transformed into this equation. This paper claims that the natural logarithm can be represented by the Gaussian hypergeometric function.
http://www.ssrn.com/abstract=3037643
http://www.ssrn.com/1626087.htmlMon, 18 Sep 2017 08:42:43 GMT