Open Research Index

B. C. Carlson's approach to special functions of applied mathematics

Bastiaan J Braams

Palomar Registrypalomar/PALOMAR-2026-09-15-000004Sep 15, 2026math.CAscore 0

Lean formalization of selected results in B. C. Carlson's theory of special functions as complex Dirichlet averages. The registry selection establishes joint entire-parameter continuation of holomorphic averages on convex open scalar domains; joint holomorphy and native-integral agreement for the Gamma-regularized R and L functions on principal slit-node domains; Euler inversion and Euler-Poisson equations; and Gamma-regularized adaptations of both quadratic R transformations for all complex exponent and Dirichlet parameters with positive-real-part unsquared variables. The L function is…

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