I've got different resources doing different things for er-hua, e.g.:
包儿
resource material #1
[pər]
resource material #2
[pɚ]
is [ɚ] and [ər] interchangeable for (儿化) er-hua?
I would hazard to guess that [ər] is just a lazy [ɚ].
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They should be the same. It is just differences in notation. [ər] is commonly used by Sinologists, while [ɚ] is actual IPA.
In the Beijing dialect (and standard Mandarin), 包儿 should be pronounced as something like [paʊɻ] (probably written by Sinologists as [paur]). It looks like you're looking at something like Sichuanese, where 包儿 is pronounced as [pɚ].
Take a look at the Wikipedia article on erhua for more details.
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@user3306356 It's just a modified version of IPA used by many Chinese scholars. Books using this type of notation would just call this IPA (broad transcription). – justinrleung Mar 24 '17 at 3:32
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NO, [ɚ][ər] are interchangeable in the case of (儿化) er-hua because 儿 comes first. In other case, when 儿 comes last, then they are interchangeable, for instance, 包儿，花儿。
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The first: [ɚ]=[ər]=[ə^ɹ(as e^x )] [ər] for print convenience. The second: 包儿 is [paur]
