Cetin Hakimoglu-Brown

collaborators

5 papers

math.NT2026

$_{5} F_{4}$ evaluations and a family of $π^{2} + lo g^{2}$ identities

Cetin Hakimoglu-Brown

We evaluate the series $\sum_{n \geq 1} z^{n} / (n^{2} (n 4 n))$ , equal to $-\tfrac{z}{4}\,{}_5F_4\!\left(1,1,1,\tfrac43,\tfrac53;\tfrac54,\tfrac32,\tfrac74,2;\tfrac{27z}…

math.CA2026

Functional Dilogarithm Identities in Quadratic Fields

Cetin Hakimoglu-Brown

We derive three- and six-term functional dilogarithm identities whose arguments lie in $Q (u, 4 - 3 u^{2})$ and $Q (u, u (4 - 3 u))$ . Our approach is based on an…

math.CA2026

On a $_{2} F_{1} (\frac{1}{4})$ -identity due to Gosper

Cetin Hakimoglu-Brown

It is only in exceptional cases that a $_{2} F_{1} (z)$ -series with rational parameters and a rational argument, apart from the cases for $z \in {\pm 1, \frac{1}{2}}$ associated with…

math.NT2026

On a conjecture due to Kanade related to Nahm sums

Cetin Hakimoglu-Brown

Kanade explored the construction of modular companions to $q$ -series identities, using the asymptotics of Nahm sums, and Mizuno [Ramanujan J.\ {\bf 66} (2025), Paper No.\ 62, 31] r…

math.NT2025

Analytic Dilogarithm Identities

Cetin Hakimoglu-Brown

We introduce dilogarithm identities through a beta integral-based technique that we apply to provide analytic proofs of previously conjectured dilogarithm relations, solving open p…

5​F4​ evaluations and a family of π2+log2 identities

Functional Dilogarithm Identities in Quadratic Fields

On a 2​F1​(41​)-identity due to Gosper

On a conjecture due to Kanade related to Nahm sums

Analytic Dilogarithm Identities

$_{5} F_{4}$ evaluations and a family of $π^{2} + lo g^{2}$ identities

On a $_{2} F_{1} (\frac{1}{4})$ -identity due to Gosper