I‘m trying to understand this equality: <mstyle displaystyle="true" scriptlevel="0">

cazinskup3

cazinskup3

Answered question

2022-06-18

I‘m trying to understand this equality:
e z + z 1 = n = ( m = 0 1 ( m + n ) ! m ! ) z n

Answer & Explanation

gaiageoucm5p

gaiageoucm5p

Beginner2022-06-19Added 20 answers

We have
e z e z 1 = j z j j ! k z k k ! = j , k z j k j ! k ! = n , k z n ( n + k ) ! k ! = n ( k 1 ( n + k ) ! k ! ) z n
where n = j k so j = n + k. The sums are taken over j, k and n varying on Z

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