X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fftc%2FMoreFunSeries.ma;h=20eaa0dcd1518073117988d91ad7f0c76c9dcd51;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=0aae72baaf58770db90e4e755819290d45dddd97;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma index 0aae72baa..20eaa0dcd 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunSeries". +include "CoRN.ma". + (* $Id: MoreFunSeries.v,v 1.4 2004/04/23 10:00:59 lcf Exp $ *) -(* INCLUDE -FunctSeries -*) +include "ftc/FunctSeries.ma". -(* INCLUDE -MoreFunctions -*) +include "ftc/MoreFunctions.ma". (*#* printing FSeries_Sum %\ensuremath{\sum_{\infty}}% #∑'# *) @@ -54,35 +52,35 @@ Some of the definitions do not make sense in this more general setting but the ones which do we simply adapt in the usual way. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/F.var. +inline "cic:/CoRN/ftc/MoreFunSeries/F.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". -inline cic:/CoRN/ftc/MoreFunSeries/contF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con". (*#* The equivalences between these definitions still hold. *) -inline cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con". (* UNEXPORTED End Definitions. @@ -96,21 +94,21 @@ Section More_Definitions. Limit is defined and works in the same way as before. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/conv.var. +inline "cic:/CoRN/ftc/MoreFunSeries/conv.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con". (* UNEXPORTED End More_Definitions. @@ -125,33 +123,33 @@ Section Irrelevance_of_Proofs. Proofs are irrelevant as before---they just have to be present. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/F.var. +inline "cic:/CoRN/ftc/MoreFunSeries/F.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/contF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". -inline cic:/CoRN/ftc/MoreFunSeries/contF0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con". (* UNEXPORTED End Irrelevance_of_Proofs. @@ -165,55 +163,55 @@ Opaque Cauchy_fun_seq_Lim_IR. Section More_Properties. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/g.var. +inline "cic:/CoRN/ftc/MoreFunSeries/g.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var". -inline cic:/CoRN/ftc/MoreFunSeries/contg.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". -inline cic:/CoRN/ftc/MoreFunSeries/contg0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contg0.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/F.var. +inline "cic:/CoRN/ftc/MoreFunSeries/F.var". -inline cic:/CoRN/ftc/MoreFunSeries/G.var. +inline "cic:/CoRN/ftc/MoreFunSeries/G.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/contF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". -inline cic:/CoRN/ftc/MoreFunSeries/contF0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var". -inline cic:/CoRN/ftc/MoreFunSeries/contG.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contG.var". -inline cic:/CoRN/ftc/MoreFunSeries/contG0.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contG0.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con". (* UNEXPORTED End More_Properties. @@ -232,45 +230,45 @@ Section Algebraic_Properties. Algebraic operations still work well. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/g.var. +inline "cic:/CoRN/ftc/MoreFunSeries/g.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". -inline cic:/CoRN/ftc/MoreFunSeries/contg.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". -inline cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/F.var. +inline "cic:/CoRN/ftc/MoreFunSeries/F.var". -inline cic:/CoRN/ftc/MoreFunSeries/G.var. +inline "cic:/CoRN/ftc/MoreFunSeries/G.var". -inline cic:/CoRN/ftc/MoreFunSeries/contF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". -inline cic:/CoRN/ftc/MoreFunSeries/contG.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contG.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/convF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". -inline cic:/CoRN/ftc/MoreFunSeries/convG.var. +inline "cic:/CoRN/ftc/MoreFunSeries/convG.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con". (* UNEXPORTED End Algebraic_Properties. @@ -284,39 +282,39 @@ Section More_Algebraic_Properties. If we work with the limit function things fit in just as well. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/g.var. +inline "cic:/CoRN/ftc/MoreFunSeries/g.var". -inline cic:/CoRN/ftc/MoreFunSeries/contf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". -inline cic:/CoRN/ftc/MoreFunSeries/contg.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/Hf.var. +inline "cic:/CoRN/ftc/MoreFunSeries/Hf.var". -inline cic:/CoRN/ftc/MoreFunSeries/Hg.var. +inline "cic:/CoRN/ftc/MoreFunSeries/Hg.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con". (* UNEXPORTED End More_Algebraic_Properties. @@ -331,15 +329,15 @@ Section Other. Finally, we define a mapping between sequences of real numbers and sequences of (constant) functions and prove that convergence is preserved. *) -inline cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con. +inline "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con". -inline cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con". (*#* Another interesting fact: if a sequence of constant functions converges then it must converge to a constant function. *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con". (* UNEXPORTED End Other. @@ -356,35 +354,35 @@ We now consider series of functions defined in arbitrary intervals. Convergence is defined as expected---through convergence in every compact interval. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/H.var. +inline "cic:/CoRN/ftc/MoreFunSeries/H.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con". (*#* Assume [h(x)] is the pointwise series of [f(x)] *) (* begin hide *) -inline cic:/CoRN/ftc/MoreFunSeries/h.con. +inline "cic:/CoRN/ftc/MoreFunSeries/h.con". (* end hide *) -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con". (* UNEXPORTED End Series_Definitions. @@ -398,15 +396,15 @@ Implicit Arguments FSeries_Sum [J f]. Section More_Series_Definitions. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". (*#* Absolute convergence still exists. *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con". (* UNEXPORTED End More_Series_Definitions. @@ -420,17 +418,17 @@ Section Convergence_Results. As before, any series converges to its sum. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con. +inline "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con". -inline cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con. +inline "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con". -inline cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con. +inline "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con". (* UNEXPORTED End Convergence_Results. @@ -453,58 +451,58 @@ Section Operations. Convergence is well defined and preserved by operations. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/g.var. +inline "cic:/CoRN/ftc/MoreFunSeries/g.var". -inline cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/convF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". -inline cic:/CoRN/ftc/MoreFunSeries/convG.var. +inline "cic:/CoRN/ftc/MoreFunSeries/convG.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con". (*#* %\begin{convention}% Let [c:IR] and [H:PartIR] be continuous in [J]. %\end{convention}% *) -inline cic:/CoRN/ftc/MoreFunSeries/c.var. +inline "cic:/CoRN/ftc/MoreFunSeries/c.var". -inline cic:/CoRN/ftc/MoreFunSeries/H.var. +inline "cic:/CoRN/ftc/MoreFunSeries/H.var". -inline cic:/CoRN/ftc/MoreFunSeries/contH.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contH.var". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con. +inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con". (* UNEXPORTED End Operations. @@ -520,19 +518,19 @@ The most important tests for convergence of series still apply: the comparison test (in both versions) and the ratio test. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/contF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". -inline cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con". -inline cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con". (* UNEXPORTED End Convergence_Criteria. @@ -551,21 +549,21 @@ $f_i$#fi# and inserting the null function in the first position. This does not affect convergence or the sum of the series. *) -inline cic:/CoRN/ftc/MoreFunSeries/J.var. +inline "cic:/CoRN/ftc/MoreFunSeries/J.var". -inline cic:/CoRN/ftc/MoreFunSeries/f.var. +inline "cic:/CoRN/ftc/MoreFunSeries/f.var". -inline cic:/CoRN/ftc/MoreFunSeries/convF.var. +inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". -inline cic:/CoRN/ftc/MoreFunSeries/insert_series.con. +inline "cic:/CoRN/ftc/MoreFunSeries/insert_series.con". -inline cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con. +inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con". -inline cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con. +inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con". -inline cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con. +inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con". -inline cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con. +inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con". (* UNEXPORTED End Insert_Series.