Abstract
We examine convergent representations for the sums of Bessel functions X∞ n=1 Jν(nx) nα (x > 0) and X∞ n=1 Kν(nz) nα (<(z) > 0), together with their alternating versions, by a Mellin transform approach. We take α to be a real parameter with ν > − 1 2 for the first sum and ν ≥ 0 for the second sum. Such representations enable easy computation of the series in the limit x or z → 0+. Particular attention is given to logarithmic cases that occur for certain values of α and ν
Original language | English |
---|---|
Pages (from-to) | 71-82 |
Number of pages | 12 |
Journal | Mathematica Æterna |
Volume | 8 |
Issue number | 2 |
Publication status | Published - 2018 |
Keywords
- Bessel functions
- Schlomilch-type series
- Mellin transform