Can Transcendental Functions be Solved Using Polynomial Equations?

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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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  • Page from a 1972 IEEE journal article titled A Near-Optimum Matching Section Without Discontinuities, showing body text, equations and a small waveguide diagram.
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  • Scanned page of a technical paper with dense mathematical text and numbered equations, including equations (4) to (12) on the Riccati and tapered transmission-line matching section.
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  • Page of a technical paper with equations on tapered transmission line matching, including integral expressions for reflection coefficient and Fourier transform relations, and a numbered equation (20) for a Dolph-Chebyshev-type ripple constant.
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  • Printed page of a journal article showing a plot of the magnitude of ripple function versus beta, labeled Fig. 2, with a dashed curve marking the optimum and several equations below for the matching section.
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  • Can Transcendental Functions be Solved Using Polynomial Equations?
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  • Scanned page of a 1971 IEEE Transactions article on microwave theory, with a small graph of return loss versus frequency and text about a Dolph-Chebyshev taper and a rectangular waveguide containing a magnetized ferrite rod.
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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.