Calculus in Coinductive Form (1998) [11 citations — 1 self]
by
D. Pavlovic
,
M.H. Escardó
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@MISC{Pavlovic98calculusin,
author = {D. Pavlovic and M.H. Escardó},
title = {Calculus in Coinductive Form},
year = {1998}
}
author = {D. Pavlovic and M.H. Escardó},
title = {Calculus in Coinductive Form},
year = {1998}
}
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Abstract:
artment of Computer Science, University of Edinburgh, Edinburgh. E-mail: mhe@dcs.ed.ac.uk tions (2) and (1) normalize the integral with respect to the subintegral function and the interval of integration. 1 Reapplying equation (3) yields the Taylor (Maclaurin) expansion f = f(0) :: f 0 = f(0) :: f 0 (0) :: f 00 . . . = f(0) :: f 0 (0) :: \Delta \Delta \Delta :: f (n) (0) :: \Delta \Delta \Delta Unfolding the above definition of ::, which amounts to iterated integration, one finally gets f(x) = f(0) + f 0 (0)x + \Delta \Delta \Delta + f (n) (0)x n<F2
Citations
| 53 | Infinite objects in type theory – Coquand - 1993 |
| 25 | Ordinary differential equations – Birkhoff, Rota - 1962 |
| 2 | Differential and Difference Equations – Brand - 1966 |
