#1613 · Real Analysis · Series

Logarithm with Quadratic Roots

If $α$ and $β$ be the roots of $x^{2} - p x + q = 0$ , show that $lo g_{e} (1 + p x + q x^{2}) = (α + β) x - \frac{α ^{2} + β ^{2}}{2} x^{2} + \frac{α ^{3} + β ^{3}}{3} x^{3} - \dots$ .

~15 minProof · checked by AIRoots of a quadraticLogarithmic series

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 17

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