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Fractional Calculus
👉The 𝑛ᵗʰ derivative can be generalized to the 𝑞ᵗʰ derivative, where 𝑞 is a rational number
👉For polynomials 𝑥ⁿ, this is done by replacing the factorial function with its continuous generalization: the Γ-function
👉The 𝑛ᵗʰ derivative can be generalized to the 𝑞ᵗʰ derivative, where 𝑞 is a rational number
👉For polynomials 𝑥ⁿ, this is done by replacing the factorial function with its continuous generalization: the Γ-function
☝️The fractional derivative of course returns the usual derivative when the derivative "powers" add up to an integer
This extension allows us to ask what happens when we take the "negative oneth" derivative
👉We would like to obtain the "left-cancellation" property of the derivative
👉To do this we are forced into the definition that the "negative oneth" derivative being the antiderivative
👉We would like to obtain the "left-cancellation" property of the derivative
👉To do this we are forced into the definition that the "negative oneth" derivative being the antiderivative
The half-derivative of eˣ
