Recurrences Related to the Bessel Function

F. T. Howard

A chapter in Applications of Fibonacci Numbers, 1988, pp 7-16 from Springer

Abstract: Abstract For k = 0, 1, 2, … let Jk(z) be the Bessel function of the first kind. Put (1.1) $$ {(z/2)^k}/{J_k}(z) = \sum\limits_{n = 0}^\infty {{u_n}(k)\frac{{{{(z/2)}^{2n}}}}{{n!(n + k)!}}} $$ ; then if follows that u0(k) =(k!)2, and for n > 0 $$ \sum\limits_{r = 0}^n {{{( - 1)}^r}\left( \begin{array}{l} n + k \\ r + k \\ \end{array} \right)} \;\left( \begin{array}{l} n + k \\ r \\ \end{array} \right){u_r}(k) = 0 $$ .

Date: 1988
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-7801-1_2

Ordering information: This item can be ordered from
http://www.springer.com/9789401578011

DOI: 10.1007/978-94-015-7801-1_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().