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2 results

  • A Generalised Kummer-Type Transformation for the pFp(x) Hypergeometric Function

  • A. R. Miller, R. B. Paris
  • Journal:
    Canadian Mathematical Bulletin / Volume 55 / Issue 3 / 01 September 2012
    Published online by Cambridge University Press:
    20 November 2018, pp. 571-578
    Print publication:
    01 September 2012
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  • In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function $_{p}{{F}_{p}}(x)$ when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to $p\,=\,1$

  • Exact distribution of word counts in shuffled sequences

  • Part of
  • Einar Andreas Rødland
  • Journal:
    Advances in Applied Probability / Volume 38 / Issue 1 / March 2006
    Published online by Cambridge University Press:
    01 July 2016, pp. 116-133
    Print publication:
    March 2006
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  • In DNA sequences, specific words may take on biological functions as marker or signalling sequences. These may often be identified by frequent-word analyses as being particularly abundant. Accurate statistics is needed to assess the statistical significance of these word frequencies. The set of shuffled sequences - letter sequences having the same k-word composition, for some choice of k, as the sequence being analysed - is considered the most appropriate sample space for analysing word counts. However, little is known about these word counts. Here we present exact formulae for word counts in shuffled sequences.