Cover Image

On the triplicity among infinite products, infinite series, and continued fractions; and its applications to divergent series

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Sogo, Kiyoshi
Format:	Preprint
Published:	2025
Subjects:	Number Theory Mathematical Physics 40, 65
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Divergent series in Gauss's diary and their extensions
by: Sogo, Kiyoshi
Published: (2026)

Extended Landen's formulas and double product theta functions
by: Sogo, Kiyoshi
Published: (2024)

Sums of infinite series involving the Dirichlet lambda function
by: Hu, Su, et al.
Published: (2025)

Summing the curious series of Kempner and Irwin
by: Baillie, Robert
Published: (2008)

The height of an infinite parallelotope is infinite
by: Kosyak, Alexandre
Published: (2023)

An extension of Gauss's arithmetic-geometric mean (AGM) to three variables iteration scheme
by: Sogo, Kiyoshi
Published: (2024)

On the transcendence of some operations of infinite series
by: Ahallal, Sarra, et al.
Published: (2024)

Equivariant primitives of Eisenstein series for congruence subgroups
by: Duhr, Claude, et al.
Published: (2025)

The $D^6 R^4$ interaction as a Poincaré series, and a related shifted convolution sum
by: Klinger-Logan, Kim, et al.
Published: (2022)

Integrals involving arbitrary powers of the arcsine, with applications to infinite series
by: Dilcher, Karl, et al.
Published: (2025)

On path integrals for wave functions taking $p$-adic values
by: Hu, Su, et al.
Published: (2025)

On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables
by: Zubarev, Alexander P.
Published: (2025)

Theory of general theta relations, addition formulas, and theta constants identities
by: Sogo, Kiyoshi
Published: (2024)

Algebraic independence of infinite series
by: Hancl, Jaroslav, et al.
Published: (2025)

On the arithmetic of multidimensional continued fractions
by: Miska, Piotr, et al.
Published: (2025)

Hopf algebras for the shuffle algebra and fractions from multiple zeta values
by: Guo, Li, et al.
Published: (2023)

Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
by: Cao, Jie, et al.
Published: (2025)

A linear independence criterion for certain infinite series with polynomial orders
by: Kudo, Shinya
Published: (2024)

Regularized products of Gauss and Eisenstein integers and primes
by: Krapivsky, P. L., et al.
Published: (2025)

On Validated Numeric of Values of Some Zeta and L-functions, and Applications
by: Glazunov, Nikolaj M.
Published: (2000)

Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
by: Liu, Wencai, et al.
Published: (2025)

Certain infinite products in terms of MacMahon type series
by: Jin, Seokho, et al.
Published: (2024)

Summing divergent matrix series
by: Wang, Rongbiao, et al.
Published: (2024)

Maximizing weighted sums of binomial coefficients using generalized continued fractions
by: Glasby, S. P., et al.
Published: (2023)

Plateaux of probability for the expanded quantum infinite well
by: Chamizo, Fernando, et al.
Published: (2024)

A series involving a product of four consecutive harmonic numbers
by: Chen, Wilson J., et al.
Published: (2025)

On the series expansion of k-free Dirichlet series and its analytical continuation
by: Kawalec, Artur
Published: (2026)

Computing the spectrum and pseudospectrum of infinite-volume operators from local patches
by: Hege, Paul, et al.
Published: (2024)

An example of path integral reduction for a simple symmetric mechanical system on a product manifold
by: Storchak, S. N.
Published: (2025)

Best approximation results for fuzzy-number-valued continuous functions
by: Font, Juan J., et al.
Published: (2025)

Epstein vector zeta functions related to the ADE Lie algebras
by: Olshanetsky, M.
Published: (2026)

Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series
by: Au, Kam Cheong
Published: (2020)

Identities and transformations for Lambert series and double Lambert series
by: Cui, Su-Ping, et al.
Published: (2026)

2d Sinh-Gordon model on the infinite cylinder
by: Guillarmou, Colin, et al.
Published: (2024)

Vanishing coefficients in two $q$-series related to Legendre-signed partitions
by: Daniels, Taylor
Published: (2024)

A splitting higher order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped
by: Ducomet, Bernard, et al.
Published: (2013)

The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip
by: Ducomet, Bernard, et al.
Published: (2013)

Transcendence criteria for multidimensional continued fractions
by: Accossato, Federico, et al.
Published: (2025)

Integer continued fractions for complex numbers
by: O'Sullivan, Cormac
Published: (2025)

Jacob's ladders, next equivalents of the Fermat-Wiles theorem and new infinite sets of the equivalents generated by the Dirichlet's series
by: Moser, Jan
Published: (2025)