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 Jan 8 awarded Student Jan 7 revised Estimated solution to system of equations with phase-shifted functions deleted 4 characters in body 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