History
The first results concerning binomial series for other than positive-integer exponents were given by Sir Isaac Newton in the study of areas enclosed under certain curves. Extending work by John Wallis who calculated such areas for y = (1 − x2)n with n = 0, 1, 2, 3, ... he considered fractional exponents. He found for such exponent m that (in modern formulation) the successive coefficients ck of (−x2)k are to be found by multiplying the preceding coefficient by (as in the case of integer exponents), thereby implicitly giving a formula for these coefficients. He explicitly writes the following instances
The binomial series is therefore sometimes referred to as Newton's binomial theorem. Newton gives no proof and is not explicit about the nature of the series; most likely he verified instances treating the series as (again in modern terminology) formal power series. Later, Niels Henrik Abel treated the subject in a memoir, treating notably questions of convergence.
Read more about this topic: Binomial Series
Famous quotes containing the word history:
“False history gets made all day, any day,
the truth of the new is never on the news
False history gets written every day
...
the lesbian archaeologist watches herself
sifting her own life out from the shards she’s piecing,
asking the clay all questions but her own.”
—Adrienne Rich (b. 1929)
“The history of all countries shows that the working class exclusively by its own effort is able to develop only trade-union consciousness.”
—Vladimir Ilyich Lenin (1870–1924)
“It is the true office of history to represent the events themselves, together with the counsels, and to leave the observations and conclusions thereupon to the liberty and faculty of every man’s judgement.”
—Francis Bacon (1561–1626)