Parabolic Cylinder Function Calculator
Free online parabolic cylinder 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：抛物柱面函数在线计算器
抛物柱面函数 Dν(z) 是韦伯方程 y'' + (ν + 1/2 − z²/4)y = 0 的标准解，也是量子谐振子薛定谔方程的数学骨架：第 n 个定态波函数正比于 Dn(√2 x/ℓ)。整数阶时三项递推 Dν+1(z) = z·Dν(z) − ν·Dν−1(z) 从 D0 = e^(−z²/4)、D1 = z·e^(−z²/4) 出发即可生成全部值。
低阶闭式：D2(z) = (z²−1)e^(−z²/4)、D3(z) = (z³−3z)e^(−z²/4)、D4(z) = (z⁴−6z²+3)e^(−z²/4)、D5(z) = (z⁵−10z³+15z)e^(−z²/4)，可作交叉校验。
参考值
D0(2) = e^(-1) = 0.36787944117144233
D5(2) = -18/e = -6.621829941085962（序列 0.367879 → 0.735759 → 1.103638 → 0.735759 → -1.839397 → -6.621830）
Dν(0)：仅偶数阶非零，D(2m)(0) = (−1)^m·(2m−1)!!
How to use the Parabolic Cylinder 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 Parabolic Cylinder 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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