Is there an alternative to Taylor series but with differences?

[Rfael69]

is there an equivalent to taylor series but with differences instead of derivatives ? are Newton series analogue to Taylor series ?

 

[fresh_42]

is there an equivalent to taylor series but with differences instead of derivatives ? are Newton series analogue to Taylor series ?

I wouldn't call it equivalent, but we have to use differences if we calculate derivatives numerically. See
https://en.wikipedia.org/wiki/Numerical_differentiation
and the links and references therein. If we use e.g. Newton series we have to deal with the error margins as with every other algorithm that computes an analytical value.

Differences and derivatives are closely related and there are likely pdf or textbooks you can find dealing with that relationship. Unfortunately, I haven't any particular knowledge in that field.

 

[jasonRF]

There is something that is sometimes described as 'difference calculus'. The equivalent to a Taylor series would be the interpolating polynomial. See, for example,

https://encyclopediaofmath.org/wiki/Finite-difference_calculus

Hamming's Numerical Methods for Scientists and Engineers has a little on this, but I wouldn't purchase the book just for that. But if you find yourself doing practical numerics at times, I have found it to be a really useful book. My copy is literally falling apart from many years of use...