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5.8.1 Limits and Series Expansion

46D006 ^LIMIText
46E006 ^REWRITEIFINF
46F006 ^SYMTAYLOR ( symb id %/z → symb )
Taylor series expansion around point 0 (McLaurin's series) with regard to given variable, and of the given order.
470006 ^SYMPAPRX
471006 ^TRUNCDL ( DL-l reste-l → truncated_DL )
Series expansion truncation.
472006 ^LIMSERIES! ( expression X=a|X %|zint → )
a lim DL-l rest-l num-l/deno-l equiv-l lvar #
Series expansion. #=1 for X=a-h or X=-1/h.
473006 ^LIMITX!
474006 ^LIMITNOVX!
475006 ^LIMERR0!
476006 ^LIMERR1!
477006 ^LIMIT! ( symb → DL-l reste-l num-l/deno-l equiv.-l lim. lvar flag )
lim. = { symf direction }
478006 ^LIMSTEP1! ( symb → { DL-l reste-l num-l/deno-l equiv.-l } flag )
479006 ^LIMSTEP2!
47A006 ^LIMSTEP3!
47B006 ^LIMSTEP4!
47C006 ^LIMLIM! ( # lvar equiv-l → lvar lim )
47D006 ^n{}N
47E006 ^LIMLIM1!
47F006 ^LIMCMPL! ( reste-1-l reste-2-l → reste-l )
480006 ^LIMEQUFR! ( n/d # → n/d-l equiv % )
481006 ^LIMEQU! ( {} # → {} / {}-equiv-l {}-equiv-l { # # # } )
482006 ^LIMEQU0!
483006 ^LIM+-! ( DL1...DLn #n op → DL flag )
DL = { DL-l reste-l num-l/deno-l equiv-l }.
484006 ^LIMERR10!
485006 ^LIMNEG!
486006 ^LIMRAC!
Racine carree, donc independant de x.
487006 ^LIMINV!
488006 ^LIM/!
489006 ^LIMPOW!
48A006 ^LIMSQ!
48B006 ^LIM*!
48C006 ^LIMDIVPC! ( #ordre num-l deno-l → num-l deno-l )
48D006 ^DIVPC!
48E006 ^LIMPROFEND! ( num deno #prof → num deno )
48F006 ^LIMPROF!
490006 ^LIM%#! ( num-l deno-l {%...%} → num-l' deno-l' #prof {%...%} )
491006 ^LIMPROF0!
492006 ^LIMPROF1!
493006 ^LIMPROF2!
494006 ^LIMINVLN!
Operator INV[-LN].
495006 ^LIMLN!
Operator LN.
496006 ^LIMEXP!
497006 ^LIMSINCOS!
498006 ^LIMATAN!
499006 ^LIMASIN!
49A006 ^LIMSQRT!
49B006 ^LIMFLOOR!
49C006 ^LIMABS!
49D006 ^LPROF!
49E006 ^LIM#VARX! ( lvar lvar → #varx )
49F006 ^LIMBETA!
4A0006 ^LIMALPHA!
4A1006 ^HORNEXP! ( lim lvar X-l reste-l → lvar DL reste-l )
4A2006 ^HORNCOS!
4A3006 ^HORNSIN!
4A4006 ^LIMSC0!
4A5006 ^LIMSC1!
4A6006 ^HORNATAN!
4A7006 ^LIMATAS!
4A8006 ^HORNASIN!
4A9006 ^HORNASIN1!
4AA006 ^HORNLN!
4AB006 ^LNOBJ!
4AC006 ^NEWLIMHORN
4AD006 ^LIMHORN!
4AE006 ^LRDM!
4AF006 ^LIMDL!
4B0006 ^LIMDLINF!
4B1006 ^LIMINFSIGN!
4B2006 ^LIMMAX!
4B3006 ^LIMCOMP!
4B4006 ^VARCOMP2!
4B5006 ^LIMSORT!
4B6006 ^VARCOMP! ( var1 var2 → flag )
4B7006 ^VARCOMPLN!
4B8006 ^VARCOMP3!
4B9006 ^VARCOMP31!
4BA006 ^VARCOMP32! ( var → 0: )
4BB006 ^VARCOMP33!
4BC006 ^LIMERR6!
4BD006 ^LIMVALOBJ! ( ob lvar → symb )
4BE006 ^LIMVAL! ( ob → coeff val )
4BF006 ^EQUIV! ( {} lequiv → equiv ordre )
4C0006 ^LVARXNX2! ( ob → ob lvarx lvarnx )
4C1006 ^SIMP1!
4C2006 ^FindCurVar ( symb → symb )
Sets a new current var if needed.
4C3006 ^LIMVAR! ( symb → symb lvar )
4C4006 ^VAR%
15C006 ^RISCH13 ( {}/{}' → {}" )
Assuming {}' has length 1, divides all elements of {} by this element. Used by RISCHext and by SERIES to have a nicer output of series.


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This document was generated by Carsten Dominik on May, 30 2005 using texi2html