On the differential transcendentality of the Morita p-adic gamma function

TL;DR

This paper proves that the Morita p-adic gamma function is differentially transcendental over the field of complex p-adic functions for any prime p, highlighting its complex algebraic independence.

Contribution

It establishes the differential transcendentality of the Morita p-adic gamma function for all primes, a novel result in p-adic analysis.

Findings

Proves differential transcendentality of mma_p over bC_p(X) for all primes p.

Extends understanding of algebraic independence in p-adic special functions.

Provides new insights into the nature of p-adic gamma functions.

Abstract

In this note we prove that for any given prime number $p$ the Morita $p$-adic gamma function $\Gamma_p$ is differentially transcendental over $\mathbb{C}_p(X)$.