convergence is simply the convergence of the sequence of partial sums.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/f.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition.
(* begin show *)
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/H.var
+*)
(* end show *)
Section More_Definitions
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var
+*)
(*#* A series can also be absolutely convergent. *)
All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/Hab.var
+*)
(* begin hide *)
(* begin show *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/g.var
+*)
(* end show *)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convG.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/c.var
+*)
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/H.var
+*)
-alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/contH.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma.
Section More_Operations
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/f.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma.
Section Other_Results
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/f.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var
+*)
(*#*
The following relate the sum series with the limit of the sequence of
Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var
+*)
(* UNEXPORTED
Opaque Frestr.