If the fundamental period of a continuous non-zero function \(f(x)\) satisfying
\[\large f(x+1)+f(x-1)=\sqrt{\pi}.f(x)\]
is \(a_1a_2a_3a_4a_5a_6a_7.b_1b_2b_3b_4b_5b_6b_7\), find the value of \(\displaystyle \sum_{i=1}^7 (a_i+b_i)\).
Assumptions:
Round off your answer up to 7 decimal places.
\(0 \leq a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7 \leq 9\)
\(\{a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7\} \in \mathbb{Z}\)
by
Sandeep Bhardwaj
