Johan Jensen (source code)

= Johan Jensen
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{wiki=Johan_Jensen_(mathematician)}

<Johan Jensen> was a <mathematician> and engineer whose work included <convex functions>, infinite <series> and <complex analysis>. His 1906 work on <convex functions> established the inequality now known as <Jensen's inequality>. He also related the zeros of a holomorphic function to the average of the logarithm of its absolute value around a circle.https://mathshistory.st-andrews.ac.uk/Biographies/Jensen/[Biography, formula for zeros and 1906 convexity paper]{ref} A basic instance of <Jensen's inequality> is $(\mathbb E X)^2\leq\mathbb E(X^2)$ for a real random variable with a finite second moment. Thus applying a convex function after averaging gives no larger a result than averaging after applying that function.

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