DOI: 10.1002/mma.9939 ISSN: 0170-4214

Summing Sneddon–Bessel series explicitly

Antonio J. Durán, Mario Pérez, Juan Luis Varona
  • General Engineering
  • General Mathematics

We sum in a closed form the Sneddon–Bessel series where is an integer, with and are the zeros of the Bessel function of order  . In most cases, the explicit expressions for these sums involve hypergeometric functions . As an application, we prove some extensions of the Kneser–Sommerfeld expansion. For instance, we show that if and (here, denotes the Bessel function of the second kind), which becomes the Kneser–Sommerfeld expansion when .

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