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10751
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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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