# Do you know its property? -11

Algebra Level 5

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:

• $$0 \leq a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7 \leq 9$$
• $$\{a_1,a_2,a_3,a_4,a_5,a_6,a_7,b_1,b_2,b_3,b_4,b_5,b_6,b_7\} \in \mathbb{Z}$$