Jinc Function Calculator
Free online jinc function calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：jinc 函数在线计算器
jinc 函数 jinc(x) = 2J₁(x)/x 是一阶 Bessel 函数的归一版本（类比 sinc = sin x/x），是圆孔夫琅禾费衍射的振幅分布：光学里著名的艾里斑图样就是 jinc²，圆盘傅里叶变换的精确结果。它同时是二维单位圆盘的径向低通滤波核，在图像重建与无线电天线方向图中出现。
级数实现：jinc = Σ (−1)^k (x/2)^(2k)/(k!(k+1)!)，递推因子 −(x²/4)/(k(k+1))。三个独立锚点：x = 1 与权威值一致、x = 5 与权威值一致、x = j₁,₁（J₁ 的第一个零点 3.8317059702075125）处结果为 0（1e-9 容差）——第三条同时验证了艾里斑暗环的位置。
参考值
jinc(0) = 1，jinc(0.5) = 0.9690738306994956，jinc(1) = 0.8801011714898670
jinc(5) = −0.1310316550365865（第一暗环内的负振幅）
第一零点 x = 3.8317059702075125 = J₁ 的第一个正零点 j₁,₁
How to use the Jinc Function Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Jinc Function Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-28
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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