Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differentiating Bessel Functions

  1. Apr 4, 2006 #1
    Hi all,

    I was just wondering if anyone knew how to differentiate Bessel functions of the second kind? I've looked all over the net and in books and no literature seems to address this problem. I don't know if its just my poor search techniques but any assistance would be appreciated.
  2. jcsd
  3. Apr 4, 2006 #2


    User Avatar

    Staff: Mentor

    Try here -


    if one can differentiate Bessel's function of first kind, then one can differentiate Bessel's function of first kind.

    See bottom of -

    or try to find there references

    Abramowitz, M. and Stegun, I. A. (Eds.). "Bessel Functions and ." §9.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 358-364, 1972.

    Arfken, G. "Neumann Functions, Bessel Functions of the Second Kind, ." §11.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 596-604, 1985.

    Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 625-627, 1953.

    Otherwise, I may have a reference elsewhere that might have exactly what you need.
  4. Apr 4, 2006 #3
    I knew there'd be some web references to make me look silly. Thank you very much for your help.
  5. Apr 4, 2006 #4


    User Avatar

    Staff: Mentor

    Some identities for Bessel's functions in terms of Jn(z), but also valid for Yn(z)

    (2n/z) Jn(z) = Jn-1(z) + Jn+1(z),

    2 d[Jn(z)]/dz = Jn-1(z) - Jn+1(z),

    d J0(z) / dz = - J1(z)

    Jn(z) Yn-1(z) - Jn-1(z) Yn(z) = 2/(pi z)

    Jn(z) d Yn(z) / dz - d Jn(z) /dz Yn(z) = 2/(pi z)
  6. May 2, 2006 #5


    User Avatar

    I'd add:


    Pretty important if you want to have the differentiated form in terms of higher order functions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Differentiating Bessel Functions
  1. Bessel function (Replies: 1)

  2. Bessel Functions (Replies: 1)

  3. Bessel Functions (Replies: 10)