Kummer Function Calculator
Free online kummer 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：合流超几何函数在线计算器
合流超几何函数 M(a, b, x) = ₁F₁(a; b; x) = Σ (a)_k/(b)_k · x^k/k!：贝塞尔、拉盖尔、厄米、Airy 全是它的特例。
一个函数覆盖半本数理方程
满足 xM″ + (b − x)M′ − aM = 0；Kummer 变换 M(a,b,x) = e^x·M(b−a, b, −x)
特例速查：M(1/2, 3/2, −x²) 与误差函数互表；拉盖尔多项式 L_n = M(−n, 1, x)（量子氢原子径向解）；厄米方程、Bessel J_ν = M(…, …, ix) 经极限合流而来。概率里 Beta 分布、非中心卡方、泊松过程置信区间都会落到 ₁F₁。数值上 |x| 大且 a、b 同号时正项级数会先冲后爆，需要 Kummer 变换挑参数较小的一支计算——这也是本工具把变换恒等式直接列进自检的原因。
How to use the Kummer 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 Kummer 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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