Several Higher Differentiation Formulas of Special Functions
نویسندگان
چکیده
The notation and terminology used in this paper are introduced in the following articles: [16], [13], [2], [3], [5], [1], [7], [9], [12], [10], [8], [18], [14], [11], [6], [15], and [17]. For simplicity, we use the following convention: x, r, a, x0, p are real numbers, n, i, m are elements of N, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. Next we state a number of propositions: (1) For every function f from R into R holds dom(f Z) = Z. (2) (−f1)−f2 = f1 f2. (3) If n ≥ 1, then dom( 1 n ) = R \ {0} and ( n)−1({0}) = {0}. (4) (r · p) 1 n = r (p 1 n ). (5) For all elements n, m of R holds n f +mf = (n+m) f. (6) If f Z is differentiable on Z, then f is differentiable on Z.
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عنوان ژورنال:
- Formalized Mathematics
دوره 16 شماره
صفحات -
تاریخ انتشار 2008