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A strange identity of an MF (Mahler function)

Wadim Zudilin

Abstract

We relate two different solutions of a Mahler equation; one solution is only defined at certain roots of unity, while the other is an analytic function inside the unit disk.

A strange identity of an MF (Mahler function)

Abstract

We relate two different solutions of a Mahler equation; one solution is only defined at certain roots of unity, while the other is an analytic function inside the unit disk.
Paper Structure (3 sections, 1 theorem, 14 equations)

This paper contains 3 sections, 1 theorem, 14 equations.

Table of Contents

  1. A Mahler function
  2. Proof
  3. Concluding remarks

Key Result

Theorem 1

For the derivatives of all orders, the function $U(q)$ agrees at every root of unity in $\Xi=\{\exp(2\pi\mathrm{i}j/2^m):j\in\mathbb Z,\ m\in\mathbb Z_{\ge0}\}$ with the radial limit of the function $U_0(q)$.

Theorems & Definitions (1)

  • Theorem 1