Trigamma Function Calculator
Free online trigamma 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：Trigamma 函数在线计算器
关键值
ψ₁(1) = π²/6；ψ₁(1/2) = π²/2；ψ₁(2) = π²/6 − 1；反射：ψ₁(1−x) + ψ₁(x) = π²/sin²(πx)
trigamma 是 digamma 的导数、gamma 的二阶对数导数 ψ₁ = ψ′ = Γ″/Γ − ψ²。贝叶斯统计里 Gamma 分布的 Fisher 信息恰是 ψ₁(shape)；随机变量「卡方分布的期望对数」经 ψ₁ 联系自由度；排队论中服务率倒数的方差估计也用它。递推 ψ₁(x+1) = ψ₁(x) − 1/x² 与 ψ 完全平行。
How to use the Trigamma 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 Trigamma 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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