Find a formula for a higher degree antiderivative

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SUMMARY

The discussion focuses on finding a formula for higher degree antiderivatives, paralleling the Fundamental Theorem of Calculus, represented as F(X)=∫f(t)dt. The conversation highlights the work of DXDeidara, who seeks a formalism to generalize these antiderivatives through the concept of differintegration, which encompasses both integer and non-integer degrees. The paper "La dérivation fractionnaire" is referenced as a key resource, detailing the notation and formalism necessary for understanding fractional calculus and its application to antiderivatives.

PREREQUISITES
  • Understanding of the Fundamental Theorem of Calculus
  • Familiarity with the concept of antiderivatives
  • Knowledge of fractional calculus
  • Basic grasp of differintegration
NEXT STEPS
  • Read "La dérivation fractionnaire" for insights on fractional calculus
  • Explore the concept of differintegration and its applications
  • Study the implications of non-integer degrees in calculus
  • Investigate advanced topics in antiderivatives and their generalizations
USEFUL FOR

Mathematicians, calculus students, and researchers interested in advanced calculus concepts, particularly those focusing on fractional calculus and generalizations of antiderivatives.

DXDeidara
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The problem asks to find a formula for a higher degree antiderivative. This formula pattern is similar to the one stated in the Fundamental Theorem of Calculus: F(X)=∫f(t)dt.

Fn(x)=∫*F(t)dt, with certain expression in the asterisk.
 
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I really don't understand what you are asking.
 
DXDeidara said:
The problem asks to find a formula for a higher degree antiderivative. This formula pattern is similar to the one stated in the Fundamental Theorem of Calculus: F(X)=∫f(t)dt.
Fn(x)=∫*F(t)dt, with certain expression in the asterisk.

I suppose that DXDeidara claims for a formalism in order to generalize the antiderivatives of higer degree (multiple integrals)
This formalism already exists in a more general background of differintegration: considering not only integer degrees, but also non integer degrees (positive or negative).
For example, see the notation page 2 (§.3) and page 3 (§.5) in the paper :
"La dérivation fractionnaire" (i.e. fractionnal calculus)
http://www.scribd.com/JJacquelin/documents
More relevant references are provided page 5, especially ref.[1]
Here, in attachment, the degree μ for antiderivatives or -μ for derivatives, can be any real number. So, the particular case of integer μ is included.
 

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