Bessel Y Function Calculator
Free online bessel y 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.
诺伊曼函数 Yᵥ(x) 是贝塞尔方程的第二个线性无关解——当物理场景在原点「不许发散」时选 Jᵥ，在原点「必须发散」（如圆柱外域、散射波、谐振腔外场）时 Yᵥ 登场。它与 Jᵥ 的组合给出汉克尔函数，是波动问题里「出射波」的标准构件。
整数阶由 Y₀ 级数与 Y₁ = −Y₀′ 逐项微分得到，再用三项递推爬升，Wronskian 恒等式全程护航。Y₀ 的小 x 主项是 (2/π)(ln(x/2)+γ)，这抹不掉的对数发散正是外域解的指纹。
参考值
Y₀(1) = 0.0882569642156766，Y₁(1) = −0.781212821300290，Y₀(5) = −0.308517625249034
半整数特例 Y(1/2)(x) = −√(2/πx)·cos x，与 J(1/2)(x) = √(2/πx)·sin x 配对
How to use the Bessel Y 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 Bessel Y 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 2026-09-27
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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