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

Cerrado
  • ¿Algo no está bien?
#2,081 1 comentario 0 reacciones 0 asignados Ver en GitHub

Los mantenedores suelen responder en 1 día

Ya se ha fusionado un pull request relacionado.

  • #2101 de @Rafael-SOWNet — fusionado

Evaluación

Dificultad
4/5
Tiempo estimado
3-5 días
Aptitud para principiantes
42/100
Tipo de issue
Error
Claridad
Bastante claro
Estado de actividad
Activo
Stack tecnológico
csharp
Área
backend-api-design

Línea de trabajo

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.

Escrito por el modelo de indexación a partir del texto del issue.

Descripción

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

Lenguaje dominante
C#
Estrellas
831
Forks
79
Merge medio
1 h 25 min
PR fusionados (30 d)
533

Preparar el entorno

Primeros pasos

  1. Lee el issue completo y luego la guía de contribución del proyecto.
  2. Comenta en el issue que vas a ocuparte — evita que dos personas hagan lo mismo.
  3. Haz un fork del repositorio y trabaja en una rama.
  4. Abre un pull request que haga referencia al número del issue.

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