List of derivatives and integrals in alternative calculi


There are many alternatives to the classical calculus of Newton and Leibniz; 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". 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, is the K-function, is subfactorial, are the generalized to real numbers Bernoulli polynomials.
Function
Derivative
Integral
Multiplicative derivative
Multiplicative integral
Discrete derivative
Discrete integral
Discrete
multiplicative derivative
Discrete multiplicative integral