6 papers
A Recursion Backbone for Circular and Elliptic Clausen Hierarchies
Ken Nagai
We introduce an elliptic extension of Clausen-type functions based on a unified recursive framework. Starting from the polylogarithmic master function, we construct a pair of circu…
Elliptic Clausen Functions and Degenerations Circular, Elliptic, and Hyperbolic Parallelism
Ken Nagai
We introduce a unified elliptic extension of CL-type Clausen functions based on logarithmic primitives of the Jacobi theta function. The resulting elliptic Clausen family satisfies…
Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives
Ken Nagai
We revisit the cyclic identities of Sun--Pan type for Bernoulli polynomials and their -analogues. From the analytic side, we formulate minimal Appell axioms that force cyclic va…
Beyond the Euler--Mascheroni Constant: A Family of Functionals
Ken Nagai
We introduce a family of regularized functionals that generalize the Euler--Mascheroni constant . They arise from a weighted regularization of Clausen-type trigonometr…
Dual Bases for Analytic Bernoulli Functions
Ken Nagai
We present a dual-basis framework for analytic Bernoulli functions. On the Hurwitz side, even zeta values arise, while on the Clausen side, odd zeta values appear. Both bases are g…
Analytic Bernoulli Functions: Correspondence with Hermite Polynomials
Ken Nagai
We establish an operator--theoretic correspondence between periodic Bernoulli kernels and Hermite polynomials, framed through the umbral calculus and a quantum analogy. Starting fr…