Infinite series | Math History | NJ Wildberger

Описание: We discuss various uses of infinite series in the 17th and 18th centuries. In particular we look at the geometric series, power series of log, the Gregory-Newton interpolation formula, Taylor's formula, the Bernoulli's, Eulers summation of the reciprocals of the squares as pi squared over 6, the harmonic series, product expansion of sinx, the zeta function and Euler's product expansion for it, the exponential function, complex values and finally the circular functions too!

Video Contents:
00:00 Infinte series
00:46 18th century mathematicians
02:40 Geometric series
03:40 Infinite polynomials
09:49 Gregory Newton Interpolation Formula
18:02 Taylor's Theorem
22:50 Leonard Euler Basel - Berlin -St Petersburg
25:11 Introduction to Analysis Infinitorum 1748
29:48 Descartes' Factor theorem
42:58 Bernoulli numbers ( James Bernoulli -Probability)
46:58 The zeta function
53:29 The Riemann Hypothesis
1:03:00 Euler's formula for complex exponential

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