Dirichlet Beta Function at Odd Positive Integers/Also presented as

Dirichlet Beta Function at Odd Positive Integers: Also presented as

This can also be expressed using the alternative form of the Euler numbers in the following form:

\(\ds \map \beta {2 n + 1}\)

\(=\)

\(\ds \dfrac {\pi^{2 n + 1} {E_n}^*} {2^{2 n + 2} \paren {2 n}!}\)

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 19$: Series involving Reciprocals of Powers of Positive Integers: $19.38$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 21$: Series of Constants: Series Involving Reciprocals of Powers of Positive Integers: $21.38.$