McLaughlin expansion is an important concept in higher mathematics, which means expanding a function into infinite series near a certain point.

Taylor expansion: f (x) = f (0)+f' (0) x+f'' (0) x 2+\ cdots+f {(n)} (0) x n+o _ n (x) f (x+f (n) (0)

2. Inverse function expansion: Taylor expansion of a function at a certain point can also be written as f (x) = f (0)+f' (0)+f' (0) (x-0) 2+\ cdots+f {(n)} (0)+f' (0). 0)2+? +f(n)(0)(x？ 0)n+on(x？ 0)。

3. Logarithm, exponent, cosine, cotangent, cotangent, residual attenuation, residual Europe, and McLaughlin formula of residual Europe. For example, for \ln( 1-x)ln( 1? X), the expansion of maclaurin is: \ ln (1-x) =-\ ln (1+x) = \ sum _ {n =1} \ dfrac {(-1). x)=？ ln( 1+x)=∑n= 1∞n(？ 1)n？ 1xn，| x | & lt； 1∣x∣<； ; 1。

Mclauren's background:

Maclaurin is a mathematician from Scotland. He was born in 1693 and grew up near Stirling, Scotland. Maclaurin, the son of a priest, was interested in mathematics since he was a child. When he was young, he entered the University of Edinburgh and got a bachelor's degree. However, he was not satisfied with this, but went on with his studies and got a doctorate.

After receiving his doctorate, Ma Kraulin began to work as a professor of mathematics in universities in Britain and continental Europe. He has extensive interests and research in the field of mathematics, including algebra, geometry and trigonometry. His research results were widely used in science, engineering and business at that time.

One of maclaurin's most famous contributions is his Theory of Flow Number published in 1748, which is one of the classic works in calculus. In this book, he expounded his understanding and application of power series, which provided important reference and enlightenment for later mathematicians.

In addition to his academic achievements, maclaurin is an outstanding educator. He devoted himself to training the younger generation of mathematicians and emphasized the understanding and application of basic concepts in his teaching. His teaching methods and thoughts had a far-reaching impact on later mathematics education.