Stieltjes Constants Calculator
Free online stieltjes constants 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.
Stieltjes 常数 γₙ 是 ζ(s) 在 s = 1 处洛朗展开的系数：ζ(s) = 1/(s−1) + Σ(−1)ⁿγₙ(s−1)ⁿ/n!。本页对 400 万项前缀和做 Euler–Maclaurin 修正。
ζ 在极点旁的"指纹"
γ₀ = 0.5772156649…，γ₁ = −0.07281584548367672486…（OEIS A073002 附近段）
调和级数减 ln N 收敛到 γ₀，但把 (ln k)ⁿ 因子放进来后残余部分就是 γₙ——它们刻画 ζ(s) 靠近 s = 1 时每一阶的弯折程度。所有 γₙ（n ≥ 1）符号无规律：γ₁、γ₂ 为负，γ₃、γ₄、γ₅ 为正，γ₆ 又转负。Kummer 定理的 ln Γ 傅里叶展开系数正是 γₙ/π 的组合，出现在解析数论与渐近分析里。
How to use the Stieltjes Constants 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 Stieltjes Constants 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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