Leonhard Euler · 1748 · Internet Archive
Introductio in analysin infinitorum
All 320 leaves · leaf 180
Transcription
152 DE ALIIS. ARCUUM ATQUE
LIB. I. necessitatem Series infinitas multiplicemus, terminos priores actu in Logarithmis involutos relinquamus, eritque
$l\sin.\frac{m\pi}{2n} = l\pi + lm + l(2n-m) + l(2n+m) - l8 - 3ln$
$-\frac{mm}{16nn} - \frac{m^4}{2.16^2 n^4} - \frac{m^6}{3.16^3 n^6} - \frac{m^8}{4.16^4 n^8} - \&c.$
$-\frac{mm}{36nn} - \frac{m^4}{2.36^2 n^4} - \frac{m^6}{3.36^3 n^6} - \frac{m^8}{4.36^4 n^8} - \&c.$
$-\frac{mm}{64nn} - \frac{m^4}{2.64^2 n^4} - \frac{m^6}{3.64^3 n^6} - \frac{m^8}{4.64^4 n^8} - \&c.$
$\&c.$
$l\cos.\frac{m\pi}{2n} = l(n-m) + l(n+
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