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April 11th, 2016, 09:01 AM   #1
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Stupid question I was thinking about...

Something just occurerd to me... We know that the Pythagorean means can be expressed elegantly as a family of means. It really amazed me when I first learnt that, because the three ostensibly unrelated expressions turned out to be able to be derived from a single expression.

My question is, for any three expressions, is it possible to find such a formula to generalise them (just as Lagrange interpolating polynomials do for numbers)? What if the expressions are purely algebraic expressions, and what if they also contain other kinds of functions (trigonometric, exponential, logarithmic, by extension hyperbolic, etc.)? Can someone point me to theories related to my question? Thanks!
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Last edited by 123qwerty; April 11th, 2016 at 09:11 AM.
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