Barnes G Function Calculator
Free online barnes g 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：Barnes G 函数在线计算器
Barnes G 函数是 Γ 函数的「下一阶」：Γ 满足 Γ(z+1) = z·Γ(z)（乘一次差分），G 满足 G(z+1) = Γ(z)·G(z)（差分多一层），于是正整数处 G(n+1) = 1!·2!·3!·…·(n−1)! —— 阶乘的阶乘（超阶乘）。它出现在函数方程的正则化行列式、随机平面划分、以及多重伽马函数的构造中。
数值上对 n ≤ 170 直接累加 ln Γ(k)（Lanczos 精度），大 n 走渐近式 ln G(n+1) ≈ n²/2·ln n − 3n²/4 + n/2·ln 2π − (1/12)·ln n + ζ′(−1) + 1/(720n²) − 1/(5040n⁴)，两者在 n = 1000 处吻合到 1e-6。
参考值
G(2) = 1，G(3) = 1，G(4) = 2，G(5) = 12，G(6) = 288，G(7) = 34560
G(1/2) ≈ 0.603244281，与 Γ(1/4) 通过反射公式关联
渐近：G(1001) = e^(lnGasym(1000))，lnG 精确值与渐近差小于 1e-6
How to use the Barnes G 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 Barnes G 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 2026-09-27
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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