List Of Derivatives And Integrals In Alternative Calculi
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There are many alternatives to the classical calculus of Newton and
Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...
; for example, each of the infinitely many non-Newtonian calculi. Occasionally an alternative calculus is more suited than the classical calculus for expressing a given scientific or mathematical idea. The table below is intended to assist people working with the alternative calculus called the "geometric calculus" (or its discrete analog). Interested readers are encouraged to improve the table by inserting citations for verification, and by inserting more functions and more calculi.


Table

In the following table; \psi(x)=\frac is the
digamma function In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: :\psi(z) = \frac\ln\Gamma(z) = \frac. It is the first of the polygamma functions. This function is Monotonic function, strictly increasing a ...
, \operatorname(x)=e^=e^ is the K-function, (!x)=\frac is subfactorial, B_a(x)=-a\zeta(-a+1,x) are the generalized to real numbers
Bernoulli polynomials In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur ...
.


See also

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Derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...
*
Differentiation rules This article is a summary of differentiation rules, that is, rules for computing the derivative of a function (mathematics), function in calculus. Elementary rules of differentiation Unless otherwise stated, all functions are functions of real nu ...
*
Indefinite product In mathematics, the indefinite product operator is the inverse operator of Q(f(x)) = \frac. It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Thus :Q\left( \prod_x f(x) \right) = f(x) \, . ...
* Product integral *
Fractal derivative In applied mathematics and mathematical analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals, defined in fractal geometry. Fractal derivatives were ...


References


External links


Non-Newtonian calculus website
{{DEFAULTSORT:Derivatives And Integrals Of Elementary Functions In Alternative Calculi Non-Newtonian calculus Mathematics-related lists Mathematical tables