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The research aims to develop a comprehensive method for analyzing inverse power Fourier-Bessel series, focusing on binomial forms and integral extensions.

February 27, 2026Open Access

Inverse Power Fourier-Bessel Series: Binomial Formulas, Integral Extensions, and Algebraic Example

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The research aims to develop a comprehensive method for analyzing inverse power Fourier-Bessel series, focusing on binomial forms and integral extensions.
Derivation of exact binomial structures for Fourier-Bessel series with finite decompositions.
Construction of integral representations using periodized Bernoulli polynomials.
Simplification of series for special values of s, leading to algebraic forms.
Exact closed-form expressions for main and residual terms of Fourier-Bessel series.
Analytic continuation of binomial formulas for s > 2π, ensuring continuity.
Reduction of series to algebraic forms for specific arguments, revealing arithmetic patterns.

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Implication

This framework shows closed-form expressions and analytic continuations in Fourier-Bessel series, suggesting new mathematical connections.

Cite This Study

Pathy (Path) Kyungu (2026) studied this question.

synapsesocial.com/papers/69a13550ed1d949a99abf172 https://doi.org/10.5281/zenodo.18777420

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Implication

This framework shows closed-form expressions and analytic continuations in Fourier-Bessel series, suggesting new mathematical connections.

Inverse Power Fourier-Bessel Series: Binomial Formulas, Integral Extensions, and Algebraic Example

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Discussion

Implication

Cite This Study

Inverse Power Fourier-Bessel Series: Binomial Formulas, Integral Extensions, and Algebraic Example

Key Points

Discussion

Implication

Cite This Study

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