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1 dzień temu · The exponential function is defined on the entire domain of the complex numbers.The definition of sine and cosine can be extended to all complex numbers via = = + These can be reversed to give Euler's formula = + = When plotted on the complex plane, the function for real values of traces out the unit circle in the complex plane.. When is a real number, sine and cosine ...
1 dzień temu · The function () is defined on the interval [,].For a given , the difference () takes the maximum at ′.Thus, the Legendre transformation of () is () = ′ (′).. In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are ...
