The Generalized Incomplete Gamma Function as sum over Modified Bessel Functions of the First Kind

  • Authors:

  • E. J. M. Veling

  • Affiliations:

  • -

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

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Abstract

We represent the Generalized Incomplete Gamma Function @C(@a,x;b)=@!"x^~t^@a^-^1exp(-t-bt)dt,@a@?R,x=0,b=0,but not both x=b=0, if @a@?0, as a sum of Modified Bessel Functions valid for non-integer @a. For integer values of @a we derive the corresponding limit case. Moreover, we discuss numerical techniques to evaluate this function.