Incomplete Bessel K function/generalized incomplete gamma function

Some mathematicians defined this type incomplete-version of Bessel function or this type generalized-version of incomplete gamma function:[1][2][3][4][5]

Properties

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One of the advantage of defining this type incomplete-version of Bessel function   is that even for example the associated Anger–Weber function defined in Digital Library of Mathematical Functions[6] can related:

 

Recurrence relations

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  satisfy this recurrence relation:

 

References

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  1. ^ "incompleteBesselK function | R Documentation". www.rdocumentation.org.
  2. ^ "incompleteBesselK: The Incomplete Bessel K Function in DistributionUtils: Distribution Utilities". rdrr.io.
  3. ^ Harris, Frank E. (2008). "Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions" (PDF). Journal of Computational and Applied Mathematics. 215: 260–269. doi:10.1016/j.cam.2007.04.008. Retrieved 2020-01-08.
  4. ^ "Generalized incomplete gamma function and its application". 2018-01-14. Retrieved 2020-01-08.
  5. ^ Didem Aşçıoğlu (September 2015). The Generalized Incomplete Gamma Functions (PDF) (Master thesis). Eastern Mediterranean University. S2CID 126117454. Archived from the original (PDF) on 2019-12-23. Retrieved 2019-12-23 – via Semantic Scholar.
  6. ^ Paris, R. B. (2010), "Anger-Weber Functions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.