Polygamma Function Calculator
Free online polygamma 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：多伽马函数在线计算器
多伽马函数 ψ⁽ᵐ⁾(x) 是 digamma（ψ）的 m 阶导数，与 Hurwitz zeta 有恒等式 ψ⁽ᵐ⁾(x) = (−1)^(m+1)·m!·ζ(m+1, x)。
符号交替的"zeta 搬运工"
ψ′(1) = π²/6 = ζ(2)；ψ″(1) = −2ζ(3) ≈ −2.4041138063；ψ′(1/2) = π²/2
偶数阶为负、奇数阶为正，绝对值全是 m!×ζ(m+1)——多伽马本质是把 zeta 的取值按阶乘加权搬运到任意点。狄利克雷分布的期望对数概率（主题模型的 E 步）、贝叶斯指数族的 KL 散度、量子力学氢原子径向解都靠它出数值。
How to use the Polygamma 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 Polygamma 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 2026-09-26
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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