Defining Closed-Form Expressions: A Scientist's Perspective

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SUMMARY

The discussion centers on the definition of closed-form expressions in mathematics, particularly regarding expressions that involve derivatives of functions. Participants agree that without a universally accepted definition of "closed form," it is challenging to classify certain expressions, especially those involving special functions with varying parameters. The ambiguity in defining well-known functions complicates the determination of whether an expression qualifies as closed-form. This uncertainty is critical for academic writing, such as in a thesis.

PREREQUISITES
  • Understanding of mathematical expressions and derivatives
  • Familiarity with the concept of closed-form expressions
  • Knowledge of special functions in mathematics
  • Experience in academic writing, particularly in mathematics
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  • Research the formal definitions of closed-form expressions in mathematical literature
  • Explore the classification of special functions and their derivatives
  • Study the implications of parameter variations in mathematical expressions
  • Review guidelines for writing a thesis in mathematics
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Mathematicians, students writing theses in mathematics, and researchers interested in the nuances of mathematical definitions and expressions.

EngWiPy
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Hello,

I have a mathematical expression that consists of a limited number of derivatives of some functions, and these derivatives exist and well defined. Can we call this expression a closed-form expression?

Regards
 
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Probably not.
Unless there is given a special definition of "closed form" .
 
g_edgar said:
Probably not.
Unless there is given a special definition of "closed form" .

The problem is: there is no agreement about the exact definition of the well known functions in the definition of the closed-form expression. I have special functions whose derivative remains the same but with different parameters. I don't know, is this closed form? I have to know to write it down in my thesis.

Regards
 

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