Can Transcendental Functions be Solved Using Polynomial Equations?

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Discussion Overview

The discussion revolves around the nature of transcendental functions and their relationship to polynomial equations. Participants seek clarification on definitions, methods for solving equations involving transcendental functions, and techniques for interpreting data from tables related to these functions.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance with solving an unspecified equation and understanding a table, indicating a need for practical application of concepts related to transcendental functions.
  • Another participant points out that the referenced equation is merely a definition of a function, suggesting that any non-polynomial function qualifies as transcendental.
  • There is a question about the method for extrapolating values from a table when the desired input is not explicitly listed, with a suggestion to fix one variable to interpolate the other.
  • A participant notes that polynomial functions must have algebraic numbers as coefficients, while those with transcendental coefficients are classified as transcendental functions.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and methods related to transcendental functions, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

The discussion lacks clarity on specific mathematical steps and definitions, which may affect the understanding of transcendental functions and their solutions.

profionus
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Hi All,

I need help to either ( in page 5 )
1) solve equation 30
2) write a program to tabulate the results in a chart
3) understand how to read table 1

regards,
profionus
 

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function

BTW,

1) what is a transendencal function anyway
2) what is the normal method to solve it

thanks
profionus
 
There's no equation in #30. It's just the definition of a function. Techincally any non polynomial function is a transcendental one.

Daniel.
 
Thanks Daniel,

May I know how you read the table 1.

If I had a value B which isn't on the graph, how do I extrapolate for the values of the function G(B,e)

regards,
profionus
 
I dunno, it's a lot more difficult, since you got a function of 2 variables, B & xi. Maybe you can fix xi to a certain value (one which is considered in the table) and then try to interpolate for an arbitrary value of B inside the intervals.

Daniel.

About transcendental functions: those polynomial functions must have algebraic numbers as coefficients. Thus, a polynomial function with transcendental coefficients is a transcendental function.

Daniel.
 

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