power series, transcendental functions, interpolation etc

Briggs (1624) first instance of binomial theorem for a fractional exponent:

    \[(1+x)^{1/2}=1+\fr{2}x-\frac{1\cdot 1}{2\cdot 4}x^2+\frac{1\cdot 1\cdot 3}{2\cdot 4\cdot 6}x^3-\frac{1\cdot 1\cdot 3\cdot 5}{2\cdot 4\cdot 6\cdot 8}x^4+\dots\]

Mercator (1668) integrated:

    \[\fr{1+x}=1-x+x^2-x^3+\dots\]

to get:

    \[log(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\dots\]


Stillwell – Mathematics and its History

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