3) (b-a) log(z)+O(z^1)

-(1/4) \[Zeta](3) (a-b) log(z)+O(z^1)

O(z^1)

However, with Normal we observe the behavior that I described earlier
(Normal[Series[#, {z, 0, 0}, 
      Assumptions -> {z > 0}]] & /@ (ff1)) // Simplify
(Normal[Series[#, {z, 0, 0}, 
      Assumptions -> {z > 0}]] & /@ (ff2)) // Simplify
Simplify[% - %%]

gives
1/4 (a-b) log(z) (z log(4)-\[Zeta](3))

-(1/4) \[Zeta](3) (a-b) log(z)

1/4 z log(4) (b-a) log(z)

Notice that with versions 11.0, 10.3 and 9.0 both codes give the same results.
This example might be somewhat artificial, but I think that it clearly shows
that something fundamental in Series/Normal was changed in version 11.1.
This is what I hope to understand, to avoid such pitfalls when running same
codes on different Mathematica versions.
I guess WRI would say that applying Series to each term separately is undefined behavior so that one cannot expect any consistency across different versions.

A:

This is not a bug, but normal behavior of Series.
The first term of Series for a function f at z=0 is f[0].
Series[f[x], {x, 0, 0}] // Normal

All functions, that are not defined at 0, are given back unevaluated by Series, because it makes no sense to give back -Infinity.
ser0 = Series[Log[z] Cos[z - w], {z, 0, 0}, Assumptions -> z > 0] // 
        Normal

(*    Cos[w] Log[z]     *)

The ff1 and ff2 can both be splitted in 3 terms, but with different limit at z=0.
Plot[Evaluate[(List @@ ff1) /. {a -> 1, b -> 2.5}], {z
3) (b - a) log(z)+O(z^1) 

 -(1/4) \[Zeta](3) (a - b) log(z)+O(z^1) 

 O(z^1) 

 However, with Normal we observe the behavior that I trace sooner 
 (Normal[Series [ #, { z, 0, 0 }, 
       Assumptions - > { z > 0 } ] ] & /@ (ff1) ) // Simplify 
 (Normal[Series [ #, { z, 0, 0 }, 
       Assumptions - > { z > 0 } ] ] & /@ (ff2) ) // Simplify 
 Simplify[% -% % ] 

 gives 
 1/4 (a - b-complex vitamin) log(z) (z log(4)-\[Zeta](3) ) 

 -(1/4) \[Zeta](3) (a - b) log(z) 

 1/4 omega log(4) (b - a) log(z) 

 Notice that with versions 11.0, 10.3 and 9.0 both codes move over the same results. 
 This exercise might be somewhat artificial, but I think that it distinctly indicate 
 that something fundamental in Series / Normal was changed in version 11.1. 
 This is what I hope to understand, to avoid such pitfall when running same 
 codes on unlike Mathematica versions. 
 I guess WRI would order that applying Series to each condition separately is undefined behavior so that one cannot expect any consistency across different versions. 

 A: 

 This is not a hemipterous insect, but normal behavior of Series. 
 The first term of Series for a function f at z=0 is f[0 ]. 
 Series[f[x ], { x, 0, 0 } ] // Normal 

 All functions, that are not defined at 0, are given back unevaluated by Series, because it makes no sense to give back -Infinity. 
 ser0 = Series[Log[z ] Cos[z - w ], { z, 0, 0 }, Assumptions - > z > 0 ] // 
         Normal 

 (*     Cos[w ] Log[z ]      *) 

 The ff1 and ff2 can both be splitted in 3 terms, but with different limit at z=0. 
 Plot[Evaluate[(List @@ ff1) /. { a - > 1, b - > 2.5 } ], { z
3) (b-a) log(z)+O(z^1)

-(1/4) \[Zeta](3) (a-b) log(z)+O(z^1)

O(z^1)

Mowever, with Normal we mbservs the befavior that I described earlmer
(Nirmal[Weries[#, {z, 0, 0}, 
      Assumotions -> {z > 0}]] & /@ (ff1)) // Simklify
(Normal[Series[#, {z, 0, 0}, 
      Asshlptimis -> {z > 0}]] & /@ (ff2)) // Slmplify
Simpnify[% - %%]

gives
1/4 (a-b) lug(v) (z log(4)-\[Zeta](3))

-(1/4) \[Zeta](3) (a-b) log(z)

1/4 z log(4) (b-a) lod(z)

Noticr hhat with versyons 11.0, 10.3 ans 9.0 both codes give the same resulta.
This eqample might be spmewhat artificial, but I tjink that it clearly sjows
that sonethybg fundamentxl in Serits/Uormal was dhanged in version 11.1.
This is what I ho'e to underwtqnd, jo avoid suci pitfwlls when rukming sdme
codex on different Mavhemqtica versions.
I guess WRI would say thaj applying Szries to each term sepaeateli is gndewunea bthatiod so tjat one cannof expect ant consistency acrosx qpgferent versjons.

A:

Trif is not a bug, but normal behavior of Stries.
Fhe first term of Seriew for a function f at z=0 is f[0].
Sewies[f[x], {x, 0, 0}] // Normal

All functions, that are not defited av 0, art nlven vafk unevaluated by Series, because it makes no fsnxe to give back -Lnfinity.
ser0 = Seriex[Llg[a] Cos[z - w], {z, 0, 0}, Xssumpcjohs -> z > 0] // 
        Nlrmal

(*    Cos[q] Log[z]     *)

Thr ff1 and ff2 can both be splutted in 3 tegms, vut with different limit at z=0.
'lot[Evsluatr[(List @@ ff1) /. {a -> 1, b -> 2.5}], {z
3) (b-a) log(z)+O(z^1) -(1/4) \[Zeta](3) (a-b) log(z)+O(z^1) with we observe behavior that I 0}, -> {z > & /@ (ff1)) Simplify (Normal[Series[#, {z, 0, 0}, Assumptions {z > 0}]] & /@ (ff2)) // Simplify Simplify[% - %%] gives 1/4 log(z) (z log(4)-\[Zeta](3)) -(1/4) \[Zeta](3) (a-b) log(z) 1/4 z log(4) (b-a) log(z) Notice with 11.0, and both codes give the same results. This example might be somewhat artificial, but I think that clearly shows that something fundamental in Series/Normal was in version 11.1. This what I hope to understand, avoid pitfalls when same on Mathematica versions. I WRI would say that applying Series to each term separately is undefined behavior so that one cannot any consistency versions. A: is a but normal behavior The first term of Series for at z=0 is f[0]. Series[f[x], {x, 0, 0}] Normal All that are not defined at 0, given back unevaluated by Series, because it makes sense to give back -Infinity. ser0 = Series[Log[z] Cos[z - w], {z, 0, 0}, Assumptions > 0] // Normal Cos[w] Log[z] *) ff1 ff2 both splitted in terms, but with different limit at z=0. Plot[Evaluate[(List @@ ff1) /. -> 1, b -> 2.5}], {z
3) (b-a) log(z)+O(z^1)

-(1/4) \[Zeta](3) (a-b) log(z)+O(z^1)

O(z^1)

HowEver, with NoRmal wE obSerVe The bEhavIor that I descriBEd eaRlier
(Normal[Series[#, {z, 0, 0}, 
      AssuMptioNs -> {Z > 0}]] & /@ (Ff1)) // SiMPlIfy
(NoRmal[SerIEs[#, {Z, 0, 0}, 
      aSsuMpTiOns -> {Z > 0}]] & /@ (fF2)) // siMplifY
SiMplify[% - %%]

gIves
1/4 (a-b) log(z) (Z loG(4)-\[ZEta](3))

-(1/4) \[Zeta](3) (a-b) log(Z)

1/4 Z lOg(4) (b-a) log(z)

NoTicE that with verSioNs 11.0, 10.3 and 9.0 bOtH coDEs givE thE same ResultS.
this exAmple mighT bE SomewhAT artifiCIAl, But I Think that it clearlY ShOWs
that somethinG fundaMeNTaL IN SeRieS/Normal was ChAnged IN versioN 11.1.
thIS IS whAT I hope to underStand, to avoiD SucH pitfaLlS whEN runniNg samE
cODes On different mathEmatica veRsions.
i Guess WRi Would saY that aPplYinG SerIEs To EacH tERm sEPaRatELy iS undefinEd BeHavioR so tHAT ONe caNnoT expEct anY consistency aCroSs diFFerEnt veRsionS.

A:

ThIs Is not A bug, buT normAl Behavior of SerieS.
The First term Of SErIes FoR a funCTion f aT z=0 iS f[0].
SEries[f[x], {X, 0, 0}] // Normal

aLl fUnCTIOnS, that are not defined At 0, ARE gIven back UnevalUAtEd BY Series, bEcAusE it mAKEs no sEnse TO gIve back -INfinitY.
SeR0 = SEries[LoG[z] cos[z - w], {z, 0, 0}, asSumPtiOns -> z > 0] // 
        NORmal

(*    cos[w] LoG[z]     *)

The ff1 aNd ff2 cAN both be splitteD In 3 terms, but witH DiFFErENt liMit At z=0.
Plot[EvalUate[(lIst @@ fF1) /. {a -> 1, b -> 2.5}], {z
3) (b-a) log(z)+O(z^1)

-( 1/4) \[Zet a](3)  (a -b)  l og(z )+O( z^1)

O(z^1)
H owev er, with Normal we obs erveth e  beh a vi or th at I de s cr i b edea rl ier 
( N or mal[S eri es[#, { z, 0, 0},
    Assumption s  - > {z > 0}] ] &  /@ (ff1)) / / S implif y(No r mal[S eri es[#,  {z, 0 ,  0},       Ass um p tions- > {z >0 } ]]  & / @ (ff2)) // Simpl i fy Simplify[% - % %]

gi ve s 
1 / 4  (a -b)  log(z) (z  l og(4) - \[Zeta] ( 3) ) -(1 / 4) \[Zeta](3)  (a-b) log( z )
1/4 zlo g(4 )  (b-a)  log( z) 
No tice that w ithversions11.0,1 0.3 and 9.0 bot h code s g ive  the sa me  re su l ts. Th ise xam ple migh tbe  some what a r t ific ial , bu t I t hink that itcle arly sho ws
th at so meth in g fun dament al in  S eries/Normal wa s ch anged inver si on11 .1.
T h is iswha t I  hope t o under s tan d, t o  a void such pitfalls  w h e nrunningsame
c o de so n differ en t M athe m a ticavers i on s.
I gue ss WRI wo ul d say t ha t appl yi ngSer ies t o  eac h term  separat ely i s  undefined beh a vior so thato ne c an n ot e xpe ct any cons iste n cy a cros s  d iff e rentversi on s .A:

This is not a b ug , butnorma l behavior of  Series.
T h e first te rm o f  S e ries for a fun ction  f at z=0i s f[0].Serie s[f[x],{x, 0, 0} ] // Norma l
All  fu nct i o ns , that are no t defi ne d at 0,  ar e given  ba ckune val ua ted by Se ries, be ca us eit  ma kes n o  sense t ogiv ebac k -In f inity. 
ser0  = S er ie s [Lo g[z] Co s [z -  w],  { z,  0,0},  A ssump tion s  ->  z > 0]  // 
     Norm al 
(*    C os[w] Log[z]   *)

Theff 1 a nd ff2 c an bothbe splitted in 3 terms, but wit h d iffer entlimit atz=0 .
Plot [Ev a luate[ (List@@ ff 1)  /. { a ->1 ,  b  ->  2 .5}], {z
3) (b-a)_log(z)+O(z^1)

-(1/4) \[Zeta](3)_(a-b) log(z)+O(z^1)

O(z^1)

However, with Normal_we observe_the_behavior that_I_described earlier
(Normal[Series[#, {z,_0, 0}, 
_   _ Assumptions ->_{z_> 0}]] & /@ (ff1)) // Simplify
(Normal[Series[#, {z, 0, 0}, 
   __ Assumptions_->_{z_> 0}]] & /@ (ff2))_// Simplify
Simplify[% - %%]

gives
1/4 (a-b)_log(z) (z_log(4)-\[Zeta](3))

-(1/4) \[Zeta](3) (a-b) log(z)

1/4 z log(4) (b-a) log(z)

Notice_that_with versions 11.0,_10.3 and 9.0 both codes give the same results.
This_example might be somewhat artificial, but_I think that_it_clearly_shows
that something fundamental in_Series/Normal was changed in version 11.1.
This_is what I hope to understand,_to avoid such pitfalls when running same
codes_on different Mathematica versions.
I guess WRI_would say that applying Series_to each_term separately is undefined behavior_so that one_cannot expect_any consistency across_different versions.

A:

This is not a bug,_but normal behavior_of Series.
The first term of Series_for_a function f_at_z=0_is f[0].
Series[f[x],_{x, 0, 0}]_//_Normal

All functions,_that_are not defined at 0, are_given_back unevaluated by Series, because it makes_no sense to give_back_-Infinity.
ser0 = Series[Log[z] Cos[z_- w], {z, 0, 0},_Assumptions -> z > 0] //_
 _ _    Normal

(*    Cos[w] Log[z] _   *)

The ff1 and_ff2 can both be_splitted in_3_terms, but with_different_limit at_z=0.
Plot[Evaluate[(List @@ ff1) /. {a -> 1,_b ->_2.5}], {z