src/HOL/Hyperreal/Series.thy
author paulson
Sat, 30 Dec 2000 22:03:47 +0100
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separation of HOL-Hyperreal from HOL-Real
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(*  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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   sumr_0   "sumr m 0 f = #0"
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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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