| Let consider (a_n )_n and (u_n )_n two reals sequence
defined such as a_0 =1 , ∀ n>1 a_(n+1) =Σ_(p=0) ^n a_p a_(n−p) and Σ_(p=0) ^n a_p u_(n−p) =0
Part1
1)Express ∀ n >1 a_n in terms of n
2) Find the largest domain of convergence of the integer serie {a_n x^n }
3)Determinate ∀ x∈D the sum f(x) of {a_n x^n }
4)Find the radius of convergence of the serie {u_n x^n }
5) Give the relation that between the sum S(x) of the second serie and (x/(f(x)))
6) Can you developp in integer serie g(x)=((πx)/(tan(πx)))
Part2
Now do the part 1 but in the order 2)−1)−3)−4)−5)−6)
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