| author | kleing |
| Sun, 24 Mar 2002 19:16:51 +0100 | |
| changeset 13067 | a59af3a83c61 |
| parent 12018 | ec054019c910 |
| child 14416 | 1f256287d4f0 |
| permissions | -rw-r--r-- |
| 10751 | 1 |
(* Title : Series.thy |
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Author : Jacques D. Fleuriot |
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Copyright : 1998 University of Cambridge |
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Description : Finite summation and infinite series |
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*) |
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Series = SEQ + Lim + |
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consts sumr :: "[nat,nat,(nat=>real)] => real" |
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primrec |
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12018
ec054019c910
Numerals and simprocs for types real and hypreal. The abstract
paulson
parents:
11701
diff
changeset
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sumr_0 "sumr m 0 f = 0" |
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ec054019c910
Numerals and simprocs for types real and hypreal. The abstract
paulson
parents:
11701
diff
changeset
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sumr_Suc "sumr m (Suc n) f = (if n < m then 0 |
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else sumr m n f + f(n))" |
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constdefs |
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sums :: [nat=>real,real] => bool (infixr 80) |
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"f sums s == (%n. sumr 0 n f) ----> s" |
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summable :: (nat=>real) => bool |
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"summable f == (EX s. f sums s)" |
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suminf :: (nat=>real) => real |
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"suminf f == (@s. f sums s)" |
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end |
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