There are many alternatives to the
classical calculus of
Newton and
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
; 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
is the
digamma function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:
:\psi(x)=\frac\ln\big(\Gamma(x)\big)=\frac\sim\ln-\frac.
It is the first of the polygamma functions. It is strictly increasing and strict ...
,
is the
K-function
In mathematics, the -function, typically denoted ''K''(''z''), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the gamma function.
Definition
Formally, the -function is define ...
,
is
subfactorial,
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
*
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. Some authors use term discrete multiplicative int ...
*
Product integral
*
Fractal derivative
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