begleitend
supplementary
Something that happens at the same time as a main thing or supplements it.
Begleitend zur Ausstellung gibt es einen ausführlichen Katalog.
As a supplement to the exhibition, there is a detailed catalog.

accompanying / supplementary
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supplementary
Something that happens at the same time as a main thing or supplements it.
Begleitend zur Ausstellung gibt es einen ausführlichen Katalog.
As a supplement to the exhibition, there is a detailed catalog.

'Begleitend' (accompanying/supplementary) is the present participle of the verb 'begleiten' (to accompany). This form is used like an adjective and describes an action that takes place at the same time as something else.
Die begleitende Musik schuf eine entspannte Atmosphäre.
The accompanying music created a relaxed atmosphere.
In this meaning, 'begleitend' (supplementary) usually refers to abstract things that supplement a main thing, such as measures, music, or information. If it is about people escorting someone, the other, literal meaning is intended.
Begleitend zum Sprachkurs erhalten die Teilnehmer Lernmaterialien.
As a supplement to the language course, participants receive learning materials.
'Begleitend' (supplementary) is often used at the beginning of a sentence in the construction 'Begleitend zu + dative' (as a supplement to + dative). The verb then follows in position two.
Begleitend zur Konferenz findet eine Fachmesse statt.
As a supplement to the conference, a trade fair is taking place.
Common nouns combined with 'begleitend' (supplementary/accompanying) are 'Maßnahmen' (measures), 'Materialien' (materials), 'Symptome' (symptoms), or 'Umstände' (circumstances).
Fieber ist ein begleitendes Symptom der Grippe.
Fever is an accompanying symptom of the flu.
simultaneously / at the same time
'gleichzeitig' and 'begleitend' can both express that something happens alongside something else. 'gleichzeitig' mainly emphasizes the same point in time: two things happen at the same time. 'begleitend' also says that something supplements or supports a main thing. It often sounds more natural with measures, courses, treatments, or information. The words can be confused when two things run in parallel. If only the timing is important, 'gleichzeitig' fits. If something is added to a main thing, 'begleitend' is more precise.

Begleitend zum Deutschkurs gibt es einmal pro Woche ein Aussprachetraining.
Alongside the German course, there is pronunciation training once a week.
Ich kann nicht gleichzeitig kochen und mit dir telefonieren.
I can't cook and talk to you on the phone at the same time.