Solving a summation equation

[drewfstr314]

Is it possible to find x such that

if you are given c and all coefficients a_n??

Thanks

 

[Deleted member 4993]

Is it possible to find x such that

if you are given c and all coefficients a_n??

Thanks

There is no general sloution after n = 4.

If you have numerical values of a_n and c, you can solve for (approximate) x through numerical analysis like Newton-Raphson alogorithm.

 

[daon2]

Not only that, there may not be a unique solution either.

For example if \(\displaystyle a_{2k+1}=0\) for all \(\displaystyle k\), then if \(\displaystyle x\) satisfies the equation, so does \(\displaystyle -x\).

 

[mmm4444bot]

if you are given … all coefficients a_n …

Are you thinking that it is possible for somebody to give you all of the coefficients?

 

[Deleted member 4993]

Are you thinking that it is possible for somebody to give you all of the coefficients?

Why not? a_n could be expressed in function form e.g. a_n = n

 

[mmm4444bot]

Oic. It's true; I never considered that the phrase "all of the coefficients" could be synonymous with the phrase "symbolic representations for all of the coefficients".

Perhaps, it was the subscripted symbol that caused me to think in terms of Real numbers. My bad.