Differentialrechnung
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|Integralcosinus | |Integralcosinus | ||
- | |<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!} | + | |<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!}+\frac{x^3}{3\cdot 3!} + \cdots,\ |x|<\infty</math> |
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|Exponentialintegral | |Exponentialintegral | ||
- | |<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = C+\ln|x|+frac x{1\cdot 1!}+\frac{x^2}{2\cdot 2!} | + | |<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = C+\ln|x|+\frac x{1\cdot 1!}+\frac{x^2}{2\cdot 2!}+\frac{x^3}{3\cdot 3!} + \cdots,\ x<0</math> |
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|Integrallogarithmus | |Integrallogarithmus | ||
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|Gaußsches Fehlerintegral | |Gaußsches Fehlerintegral | ||
- | |<math>F(x) = \frac 1{\sqrt{2\pi}}\int_{-\infty}^xe^{-\frac{t^2} 2} dt = </math> | + | |<math>F(x) = \frac 1{\sqrt{2\pi}} \int_{-\infty}^xe^{-\frac{t^2} 2} dt = \frac 1 2 + \frac 1{\sqrt{2\pi}} \left(\frac x 1-\frac{x^3}{2\cdot3\cdot1!}+\frac{x^5}{2^2\cdot5\cdot2!}-\frac{x^7}{2^3\cdot7\cdot3!}+-\cdots\right),\ |x|<\infty</math> |
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[[category:Mathematik]] | [[category:Mathematik]] |
Revision as of 09:41, 17 September 2008
Funktion | Ableitung | Integral |
Integrationsregeln
unbestimmtes Integral
Integration durch Substitution,
oder partielle Integration
weitere Integrale
Funktion | Integral |
Integralfunktionen
Integralsinus | Eulersche Konstante | |
Integralcosinus | ||
Exponentialintegral | ||
Integrallogarithmus | ||
Gaußsches Fehlerintegral |