A Note on Some Reduction Formulas for the Incomplete Beta Function and the Lerch Transcendent

Juan Luis González-Santander
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Juan Luis González-Santander: Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Spain

Mathematics, 2021, vol. 9, issue 13, 1-6

Abstract: We derive new reduction formulas for the incomplete beta function B ? , 0 , z and the Lerch transcendent ? z , 1 , ? in terms of elementary functions when ? is rational and z is complex. As an application, we calculate some new integrals. Additionally, we use these reduction formulas to test the performance of the algorithms devoted to the numerical evaluation of the incomplete beta function.

Keywords: incomplete beta function; lerch transcendent; reduction formulas; numerical evaluation of special functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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