What does this research mean for the field?

Novel recurrence relations reduce the calculation of derivatives for fundamental Bessel function ratios to tractable algebraic operations, enabling explicit derivations up to the sixth order and the generation of new infinite series. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This work aims to derive systematic formulas for the derivatives of specific Bessel function ratios. It also seeks to demonstrate practical applications in engineering problems.

June 7, 2026MathematicsOpen Access

Note on Derivatives of Bessel Function Ratios

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This work aims to derive systematic formulas for the derivatives of specific Bessel function ratios. It also seeks to demonstrate practical applications in engineering problems.
Introduced recurrence relations to simplify the calculation of derivatives for five Bessel function ratios.
Derived explicit formulas up to the sixth order for these ratios.
Applied the method to an inverse Laplace transform problem relevant to fluid mechanics.
Established a recursive framework that significantly simplifies derivative calculations from complex procedures.
Generated new infinite series based on Bessel function zeros, extending existing frameworks like the Rayleigh function.
Provided closed-form expressions for previously unaddressed cases in Pedersen’s series.

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Implication

Novel recurrence relations calculate derivatives of Bessel function ratios, enhancing engineering applications.

Cite This Study

Kamil Urbanowicz (2026) studied this question.

synapsesocial.com/papers/6a250b0e7def13d035e1b1de https://doi.org/10.3390/math14112011

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Note on Derivatives of Bessel Function Ratios

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Note on Derivatives of Bessel Function Ratios

Key Points

Discussion

Implication

Cite This Study

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