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A definite integral through a special function's limit is NaN where it has a value

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  • 哪里不对？
#2,081 1 条评论 0 个 reaction 已指派 0 人 在 GitHub 查看

维护者通常 1 天内回复

已经有一个关联 PR 被合并了。

  • #2101 来自 @Rafael-SOWNet —— 已合并

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难度
4/5
预计耗时
3-5 天
新手友好度
42/100
Issue 类型
缺陷
描述清晰度
基本清楚
活跃度
活跃
技术栈
csharp
领域
backend-api-design

调研方向

Start with the limit engine’s ComputeLimitDivideEtImpera handling for special functions and the AtTheBound behavior described in the issue. Reproduce the reported integrals involving erf, Si, and e^(x^3), then trace how an undecided bound limit affects the result. Done means undecided limits no longer turn these integrals into NaN, while the reported definite values remain obtainable.

由索引模型根据 Issue 内容生成。

描述

On 2.6.0 and on master b21f0138:

answer value
integral(ln(x)*erf(x), x, 0, 1) NaN -0.261348360021399, by quadrature
integral(ln(x)*Si(x), x, 0, 1) NaN -0.246573634234758
limit(erf(x), x, 0) left as written 0

Two causes.

  • No special function has a limit. None of #1501's functions, polygamma or gamma(a, z) overrides ComputeLimitDivideEtImpera, so the limit engine decides nothing about any of them, even where the function is continuous and the limit is its value.
  • A bound whose limit is not decided gives NaN. The antiderivative of ln(x) erf(x) is undefined at 0, as x ln(x) is. AtTheBound takes the limit there, and where it is not decided it returns the undefined value, so the integral is NaN, which says it does not exist. An undecided limit is not a claim that the integral does not exist, and the integral should be left as written.

The second is the one that answers wrongly. The first is what makes it reachable.

#2075's next rule reaches the same thing through the gamma function: integral(e^(x^3), x, 0, 1) is NaN there, where it is 1.34190441797742.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

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从这里开始

  1. 先读完整个 Issue，再读项目的贡献指南。
  2. 在 Issue 下留言说明你要接手 —— 这能避免两个人做同样的事。
  3. Fork 仓库，在一个分支上完成修改。
  4. 提交 Pull Request，并在描述里引用这个 Issue 编号。

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