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Jan
8
awarded  Student
Jan
7
revised Estimated solution to system of equations with phase-shifted functions
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Jan
5
comment $\sum_{n=0}^{\infty} \frac{1}{2n+1} = 0.66215 + \frac{1}{2}\log(\infty)^{3}$
*fall = far (typo that I'm not allowed to correct).
Jan
5
comment Finding the First Few Terms of the Sum of Two Infinite Series
That makes sense, I think. Without more knowledge the most I know to simplify this is $f(x) = \sum_{n=0}^\infty \left[ x^{n-11} \sum_{j=0}^n \left( a_{n-j} \sum_{k=0}^j d_k c_{j-k} \right) + x^{n-8} \sum_{j=0}^n e_j b_{n-j} \right] $
Jan
5
awarded  Supporter
Jan
5
comment Finding the First Few Terms of the Sum of Two Infinite Series
Am I correct in thinking that $f(x) = \sum_{n=0}^\infty \left( x^{n-11} \sum_{j=0}^n \left( a_{n-j} \sum_{k=0}^j d_k c_{j-k} \right) \right) + \sum_{n=0}^\infty \left( x^{n-8} \sum_{j=0}^n e_j b_{n-j} \right) $ ?
Jan
3
comment Is there a general solution to this phase-shifted system of equations?
For this question we can assume that the system is not underdetermined and that the number of equations matches the number of unknowns.
Jan
3
comment Is there a general solution to this phase-shifted system of equations?
You make a good point about convergence. If $|\mu| > 1$ then simply divide the previous equation by $\mu$, add $\phi$ to both function arguments and you will have a new equation for which $|\mu| < 1$.
Jan
3
comment Is there a general solution to this phase-shifted system of equations?
Added what I think is the generic recurrence solution.
Jan
3
revised Is there a general solution to this phase-shifted system of equations?
added 187 characters in body
Jan
3
asked Is there a general solution to this phase-shifted system of equations?
Jan
2
revised Estimated solution to system of equations with phase-shifted functions
added 497 characters in body
Jan
2
awarded  Editor
Jan
2
revised Estimated solution to system of equations with phase-shifted functions
added 43 characters in body
Jan
2
asked Estimated solution to system of equations with phase-shifted functions
Jan
2
awarded  Autobiographer