Several Differentiation Formulas of Special Functions. Part VI
نویسندگان
چکیده
منابع مشابه
Several Differentiation Formulas of Special Functions. Part VI
The papers [11], [13], [1], [15], [2], [8], [9], [16], [5], [12], [10], [4], [6], [7], and [14] provide the notation and terminology for this paper. In this paper x denotes a real number and Z denotes an open subset of R. One can prove the following propositions: (1) Suppose Z ⊆ dom((the function tan) ·(the function cot)). Then (i) (the function tan) ·(the function cot) is differentiable on Z, ...
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(Def. 2) cosec = 1 the function sin . For simplicity, we follow the rules: x, a, b, c are real numbers, n is a natural number, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. One can prove the following propositions: (1) If (the function cos)(x) 6= 0, then sec is differentiable in x and (sec)′(x) = (the function sin)(x) (the function cos)(x)2 . (2) If (the function s...
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The papers [13], [15], [1], [10], [16], [5], [12], [3], [6], [9], [4], [11], [8], [14], and [7] provide the terminology and notation for this paper. For simplicity, we adopt the following rules: x denotes a real number, n denotes an element of N, Z denotes an open subset of R, and f , g denote partial functions from R to R. Next we state a number of propositions: (1) Suppose Z ⊆ dom((the functi...
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The notation and terminology used here are introduced in the following papers: [13], [15], [1], [16], [2], [4], [10], [11], [17], [5], [14], [12], [3], [7], [6], [9], and [8]. For simplicity, we adopt the following convention: x, a, b, c denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2 denote partial functions from R to R. Next we state a number of ...
متن کاملSeveral Differentiation Formulas of Special Functions. Part III
The articles [13], [15], [16], [1], [4], [10], [11], [17], [5], [14], [12], [2], [6], [9], [7], [8], and [3] provide the terminology and notation for this paper. For simplicity, we follow the rules: x, r, a, b denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2, f3 denote partial functions from R to R. One can prove the following propositions: (1) x2 Z...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2007
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-007-0028-1