Introductio in analysin infinitorum

SINUUM EXPLICATIONIBUS INFINITIS. 153 CAP. XI. $l \cos \frac{m\pi}{2n} = l(n-m) + l(n+m) - 2ln$ $-\frac{mm}{nn}(\frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \frac{1}{9^2} + \&c.)$ $-\frac{m^4}{2n^4}(\frac{1}{3^4} + \frac{1}{5^4} + \frac{1}{7^4} + \frac{1}{9^4} + \&c.)$ $-\frac{m^6}{3n^6}(\frac{1}{3^6} + \frac{1}{5^6} + \frac{1}{7^6} + \frac{1}{9^6} + \&c.)$ $-\frac{m^8}{4n^8}(\frac{1}{3^8} + \frac{1}{5^8} + \frac{1}{7^8} + \frac{1}{9^8} + \&c.)$ &c. Serierum posteriorum modo ante (§. 190 ) summae sunt exhibitae; priores Series quidem ex his derivari possent, at, quo facilius ad usum transferri queant, earum summas pariter hic adjiciam. 193. Quod si ergo, brevitatis gratia, ponamus $\alpha = \frac{1}{2^2} + \frac{1}{4^2} + \frac{1}{6^2} + \frac{1}{8^2} + \&c.$ $\beta = \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \frac{1}{8^4} + \&c.$ $\gamma = \frac{1}{2^6} + \frac{1}{4^6} + \frac{1}{6^6} + \frac{1}{8^6} + \&c.$ $\delta = \frac{1}{2^8} + \frac{1}{4^8} + \frac{1}{6^8} + \frac{1}{8^8} + \&c.$ &c. erunt summae in numeris proxime expressae hae : $\alpha = 0, 41123351671205660911810$ $\beta = 0, 06764520210694613696975$ $\gamma = 0, 01589598534350701780804$ $\delta = 0, 00392217717264822007570$ $\epsilon = 0, 00097753376477325984898$ $\xi = 0, 00024420070472492872274$ Euleri Introduct. in Anal. infin. parv. V $\eta =$