Use Residus theorem to prove that ∀ a>0 Σ_(n=0) ^∞ (1/( n^2 +a^2 )) = (1/2)((π/(ash(πa))) −(1/a^2 ))
and Σ_(n=0) ^∞ (((−1)^n )/(n^2 +a^2 )) = (1/2)((( π)/(a.th(πa))) −(1/a^2 ))
Assume that we can developp in integer serie the functions
f(x)=(x/(shx)) and g(x)=(x/(thx))
Give the DL_2 of f and g around zero
Why can′t we use that theorem to explicit
f(a)=Σ_(n=0) ^∞ (((−1)^n )/( (2n+1)^2 +a^2 )) ???
help please.
A river is 5m wide and flows at 3.0ms^(−1) . A man can swim at 2.0ms^(−1)
in still water. if he sets off at an angle of 90° to the bank
calculate
a) the mans time and velocity
b) his distance downstream from the starting point till
when he reaches the other side of the river bank
c) the actual distance he swims through the water.
To conserve rice from a cooperative there is
a foil of area A=24cm^2 . The cooperatives
want to build a barn in the shape of a parallelopiped
square rectangle without cover.
What should be the symmetrical dimensions for
the volume to be maximum?