Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to find an expression for the values of the derivates of the Bessel-[tex]J_1[/tex] functions at two.

The function is defined by

[tex]J_1(x)=\sum_{k=0}^\infty{\frac{(-1)^k}{(k+1)!k!}\left(\frac{x}{2}\right)^{2k+1}}[/tex]

this I can differentiate term by term, finding for the n^th derivative at two:

[tex]J_1^{(n)}(2)=\sum_{k=\left\lfloor\frac{n}{2}\right\rfloor}^\infty{\frac{(-1)^k(2k+1)!}{(k+1)!k!(2k+1-n)!2^n}}[/tex]

Does anybody know a nice expression for this? It can probably be written as the sum of two Besselfunctions evaluated at two, but I have no idea how to find the coefficients...

Thanks

-Pere

Edit:

I found that for n even the result can be written as a linear combination of [tex]J_1(2)\text{ and } J_2(2)[/tex]. When multiplied by 2^n the coefficients are all integral ... (Experimental results).

I tried the sequence of these integers in that famous integers sequence database, but nothing ...

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differentiatiang Bessel functions

Loading...

Similar Threads - Differentiatiang Bessel functions | Date |
---|---|

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus | Saturday at 12:51 PM |

A Bessel function, Generating function | Dec 5, 2017 |

A Gamma function, Bessel function | Dec 5, 2017 |

A Coulomb integrals of spherical Bessel functions | Mar 9, 2017 |

I Integral with complex oscillating phase | Nov 16, 2016 |

**Physics Forums - The Fusion of Science and Community**