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

Mathematics

Juan Luis González-Santander¹ 

[1] Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Spain;

关键词: incomplete beta function;    lerch transcendent;    reduction formulas;    numerical evaluation of special functions;   

DOI  :  10.3390/math9131486

来源: DOAJ

【 摘 要 】

We derive new reduction formulas for the incomplete beta function $\mathrm{B}\left(\nu ,0,z\right)$ and the Lerch transcendent $\Phi \left(z,1,\nu \right)$ in terms of elementary functions when $\nu$ 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.

【 授权许可】

Unknown