References
The references below identify classical definitions, proof inputs and adjacent constructions. They do not constitute an exhaustive priority review. The arithmetic seed and the Gamma–Laguerre comparisons inherited from the project are documented in the preserved research archive.
Mendez2024
Miguel A. Méndez. Combinatorial differential operators in: Faà di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted trees. Australasian Journal of Combinatorics 89(3) (2024), 350–384. Example 2.4 contains the diagonal feedback equation. https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p350.pdf
Dascaliuc2025
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann and Edward C. Waymire. Transformation of Stochastic Recursions and Critical Phenomena in the Analysis of the Aldous-Shields-Athreya Cascade and Related Mean Flow Equations. arXiv:2411.00629v2 (2025). The nonlinear equation \(u'=-u+u(\alpha t)^2\) is an adjacent model, not the equation studied here. https://arxiv.org/abs/2411.00629v2
Coffey2006
Mark W. Coffey. On the coefficients of the Baez-Duarte criterion for the Riemann hypothesis and their extensions. arXiv:math-ph/0608050 (2006). Its signed Möbius weights differ from the positive squarefree weights used here. https://arxiv.org/abs/math-ph/0608050
DLMF
NIST Digital Library of Mathematical Functions. Sections 5.5 and 5.12 give the gamma reflection and beta identities. Section 10.46 defines the Mittag–Leffler function. Sections 16.8 and 16.21 give the generalized hypergeometric and Meijer \(G\) differential equations. Section 18.2 develops general orthogonal-polynomial theory. https://dlmf.nist.gov/
Uvarov1969
V. B. Uvarov. The connection between systems of polynomials that are orthogonal with respect to different distribution functions. USSR Computational Mathematics and Mathematical Physics 9(6) (1969), 25–36. https://doi.org/10.1016/0041-5553(69)90124-4
Elkies
Noam D. Elkies. Functions of finite order: product formula and logarithmic derivative. Harvard Math 259 course notes. The finite-order Hadamard theorem supplies the classical factorization input. https://people.math.harvard.edu/ elkies/M259.02/prod.pdf
Byrnes2013
Alyssa Byrnes, Lin Jiu, Victor H. Moll and Christophe Vignat. Recursion Rules for the Hypergeometric Zeta Functions. arXiv:1305.1892 (2013). Hypergeometric zero spectra and coefficient recursions provide related constructions. https://arxiv.org/abs/1305.1892
Voros2003
André Voros. Zeta functions for the Riemann zeros. Annales de l'Institut Fourier 53(3) (2003), 665–699. Sections 2.1–2.2 develop related canonical-product and Mellin methods. https://doi.org/10.5802/aif.1955
Voros2004
André Voros. Erratum: Zeta functions for the Riemann zeros. Annales de l'Institut Fourier 54(4) (2004), 1139. https://doi.org/10.5802/aif.2046
OEIS
The OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences, sequence A000182. This is the tangent-number anchor. No unmatched-prefix novelty claim or submission to OEIS is asserted. https://oeis.org/A000182
Alrabaiah2020
Hussam Alrabaiah, Israr Ahmad, Kamal Shah and Ghaus Ur Rahman. Qualitative analysis of nonlinear coupled pantograph differential equations of fractional order with integral boundary conditions. Boundary Value Problems 2020, article 138. This is a coupled fractional boundary-value system with different hypotheses. https://doi.org/10.1186/s13661-020-01432-2
Blasiak2011
Pawel Blasiak and Philippe Flajolet. Combinatorial Models of Creation–Annihilation. Séminaire Lotharingien de Combinatoire 65 (2011), B65c. Proposition 24 and Note 25 discuss multitype increasing trees and differential systems. https://arxiv.org/abs/1010.0354v3
Mauldin1988
R. Daniel Mauldin and S. C. Williams. Hausdorff Dimension in Graph Directed Constructions. Transactions of the American Mathematical Society 309(2) (1988), 811–829. Its spectral-radius balance describes a geometric dimension. The analytic order law here requires its own proof. https://sites.math.unt.edu/ mauldin/papers/no67.pdf
Knessl2006
Charles Knessl and Wojciech Szpankowski. Binary Trees, Left and Right Paths, WKB Expansions, and Painlevé Transcendents. Proceedings of ANALCO (2006), 198–204. The ordinary generating-function identity has different normalization and coefficient rules from the differential system here. https://www.cs.purdue.edu/homes/spa/papers/analco06.pdf
Schilling2010
René L. Schilling, Renming Song and Zoran Vondraček. Bernstein Functions: Theory and Applications. First edition. De Gruyter, 2010. ISBN 978-3-11-021530-4. Proposition 1.2 and Theorem 1.4 give the classical Laplace uniqueness and Bernstein representation results. https://doi.org/10.1515/9783110215311