I Evaluation of the sum 1^m+3^m+5^m+ ....................(2n+1)^{m}

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The discussion focuses on evaluating the sum of odd powers, specifically the series 1^m + 3^m + 5^m + ... + (2n+1)^m. It highlights the relationship between this sum and the normal sum of integers raised to the power m, noting the involvement of Bernoulli Polynomials. Participants suggest starting the evaluation by expressing (2k+1)^m as a binomial expansion. The conversation emphasizes the importance of breaking down the series into manageable components for calculation. Overall, the evaluation of this sum involves advanced mathematical concepts and techniques.
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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
 
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