how can i evaluate the sum $$
1^m+3^m+5^m+ ....................(2n+1)^{m} $$
for the case of the normal sum $$ 1^m +2^m +........................+n^, $$ for positive 'm' i know they are related to the Bernoulli Polynomials
My approach,
##(0.90)^{2.2}=(1-0.1)^{2.2}-1+\dfrac{2.2×-0.1}{1!}+\dfrac{1.2 ×2.2×(-0.1)^2}{2!}+\dfrac{0.2×1.2×2.2×(-0.1)^3}{3!}+...##
## =1-0.22+0.0132-0.000088=0.7931##
There may be other approach. Insight welcome.