arutlesidderivates
Arutlesidderivates are a hypothetical derivative-like operator used in speculative mathematics and worldbuilding contexts. They generalize the notion of differentiation by applying a fixed linear operator to a function repeatedly, producing a family of higher-order arutlesidderivatives.
Definition and notation: For a smooth function f on an interval, define ASD_0 f = f and ASD_{n+1}
Examples: If T = d/dx, then ASD_1 f = f', ASD_2 f = f'', and so on. If T =
Properties and limitations: In this framework, linearity typically holds: ASD_n(af + bg) = a ASD_n f + b ASD_n
See also: derivative, nth derivative, operator theory, generalized derivatives. References: this is a fictional construct and