Dirichlet Eta Calculator
Free online dirichlet eta 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：狄利克雷 eta 函数在线计算器
闭式与意义
η(1) = ln2；η(2) = π²/12；η(3) = 3·ζ(3)/4 ≈ 0.901542677369696；η(0) = 1/2；η(−1) = 1/4；η(−2) = 0
η(s) = (1 − 2^(1−s))ζ(s) 给 ζ 除去 s = 1 处的极点（括号因子恰为零），因此 eta 是整函数——它是「解析延拓的安全门」：1 − 1/2 + 1/3 − ⋯ 的Grandi 型发散在 η(1) = ln2 处获得 Abel 和。负偶数处 η = 0 对应 ζ 的平凡零点。
How to use the Dirichlet Eta 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 Dirichlet Eta 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.
Related calculators
More in this category: Math calculators
About math calculators
Free online math calculators for algebra, statistics, number theory and everyday arithmetic — from quadratic equations and matrices to percentages, fractions and prime factorization, each with step-by-step formulas.