Changes

*But in most of the cases <math>\alpha</math> is the non-negative real number.

*But in most of the cases <math>\alpha</math> is the non-negative real number.

*The solutions of this equation are called Bessel Functions of order n.  

*The solutions of this equation are called Bessel Functions of order n.  

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

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

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

*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>

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

*where <math>\Gamma(n+k+1)=(n+k)!</math> or   

*where <math>\Gamma(n+k+1)=(n+k)!</math> or   

*<math>\int\limits_{0}^{\infty} x^{n+k}*e^{-x} dx</math> is the Gamma Function.

*<math>\int\limits_{0}^{\infty} x^{n+k}*e^{-x} dx</math> is the Gamma Function.