Changes

*The solutions of this equation are called Bessel Functions of order <math>n</math>.  

*The solutions of this equation are called Bessel Functions of order <math>n</math>.  

*Bessel functions of the first kind, denoted as <math>Jn(x)</math>.  

*Bessel functions of the first kind, denoted as <math>Jn(x)</math>.  

*The Bessel function of the first kind of order can be expressed as:<math>Jn(x)=sum_{k=0}^\infty}\frac{(-1)^k}{k!\Gamma(n+k+1)}.(\frac{x}{2})^{n+2k}</math>

*The Bessel function of the first kind of order can be expressed as:

<math>Jn(x)=\sum_{k=0}^\infty}\frac{(-1)^k}{k!\Gamma(n+k+1)}.(\frac{x}{2})^{n+2k}</math>

 

*The Bessel function of the second kind  <math>Yn(x)</math>.

*The Bessel function of the second kind  <math>Yn(x)</math>.

*The Bessel function of the 2nd kind of order  can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}</math>

*The Bessel function of the 2nd kind of order  can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}</math>