Why must a polynomial be finite in length? Is there such thing as a

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SUMMARY

A polynomial must be finite in length because that is its defining characteristic; if it is infinite, it is classified as a power series. The discussion clarifies that recursive polynomials do not exist in standard mathematical definitions. The distinction between polynomials and power series is crucial for understanding their respective properties and applications.

PREREQUISITES
  • Understanding of polynomial definitions in mathematics
  • Familiarity with power series concepts
  • Basic knowledge of recursive functions
  • Mathematical terminology related to series and sequences
NEXT STEPS
  • Research the properties of power series and their applications
  • Explore the concept of recursive functions in mathematics
  • Study the differences between polynomials and power series
  • Investigate advanced topics in mathematical series and sequences
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Mathematicians, students studying algebra, and anyone interested in the foundational concepts of polynomials and series in mathematics.

Kidphysics
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Why must a polynomial be finite in length? Is there such thing as a recursive polynomial? Thanks guys!
 
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Kidphysics said:
Why must a polynomial be finite in length?
Well, because that's the definition. If it's infinite in length it's called a power series.

Is there such thing as a recursive polynomial? Thanks guys!
http://www.google.com/search?q=recursive+polynomial".
 
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