On arithmetic nature of special values of the incomplete beta function

Authors

• Sonika Dhillon, Indian Statistical Institute (Delhi Centre)
• Ekata Saha, Indian Institute of Technology Delhi

Article Type

Research Article

Publication Title

Acta Arithmetica

Abstract

We study the arithmetic nature of special values of the incomplete beta function Bx(a, b), defined by the integral ^x0 t^a−1(1−t)^b−1 dt for a, b > 0 and 0 ≤ x ≤ 1. For x = 1, one recovers the beta function B(a, b) = ¹0 t^a−1(1 − t)^b−1 dt, for which Schneider proved that B(a, b) is transcendental for any a, b ∈ Q \ Z such that a + b ∈/ Z. However, possible transcendental nature of special values of the incomplete beta function is a delicate question due to its relation to the Gauss hypergeometric function.

First Page

273

Last Page

284

DOI

10.4064/aa240610-6-10

Publication Date

1-1-2025

Recommended Citation

Dhillon, Sonika and Saha, Ekata, "On arithmetic nature of special values of the incomplete beta function" (2025). Journal Articles. 5486.
https://digitalcommons.isical.ac.in/journal-articles/5486