Intellectually Curious

OEIS A000134: Zeros of the Bessel function J0 rounded to the nearest integer

17 Feb 2025

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Today we explore A000134, the sequence formed by rounding the positive zeros of the Bessel function J0 to the nearest integer. The actual zeros are approximately 2.4048, 5.5201, 8.6537, 11.7915, 14.9309, …, so the rounded values are 2, 6, 9, 12, 15, … The terms grow roughly linearly with pi, reflecting the asymptotic spacing z_n ~ (n − 1/4)π and a_n ≈ round(z_n). There is no known simple closed form for a_n. The OEIS page notes an interesting question: are the differences a_{n+1} − a_n always 3 or 4? It’s a small question with a surprising connection to how zeros of Bessel functions align on the number line. Beyond the numbers, these zeros underpin many applications—from vibrating circular membranes to cylindrical waveguides—and the rounded sequence provides a compact bridge between analysis and arithmetic. Finally, we’ll touch on how these zeros are computed with high precision and why understanding their distribution matters in modeling physical systems.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information. Sponsored by Embersilk LLC

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13:00H | 21 DIC 2025 | Fin de Semana

01 Jan 1970

Fin de Semana

10:00H | 21 DIC 2025 | Fin de Semana

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12:00H | 20 DIC 2025 | Fin de Semana

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2ª PARTE | 06 ENE 2026 | EL PARTIDAZO DE COPE

01 Jan 1970

El Partidazo de COPE

3ª PARTE | 22 ENE 2026 | EL PARTIDAZO DE COPE

01 Jan 1970

El Partidazo de COPE

3ª PARTE | 04 MAR 2026 | EL PARTIDAZO DE COPE

01 Jan 1970

El Partidazo de COPE

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Intellectually Curious

OEIS A000134: Zeros of the Bessel function J0 rounded to the nearest integer

This episode hasn't been transcribed yet

Other recent transcribed episodes

13:00H | 21 DIC 2025 | Fin de Semana

10:00H | 21 DIC 2025 | Fin de Semana

12:00H | 20 DIC 2025 | Fin de Semana

2ª PARTE | 06 ENE 2026 | EL PARTIDAZO DE COPE

3ª PARTE | 22 ENE 2026 | EL PARTIDAZO DE COPE

3ª PARTE | 04 MAR 2026 | EL PARTIDAZO DE COPE

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