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Formula:3446

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Digital Library of Mathematical Functions ID 8.21.E26

f ⁢ ( a , z ) ∼ z a - 1 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ ( 1 - a ) 2 ⁢ k z 2 ⁢ k , asymptotic-expansion 𝑓 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript subscript 𝑘 0 superscript 1 𝑘 Pochhammer 1 𝑎 2 𝑘 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle f(a,z)\sim z^{a-1}\sum_{k=0}^{\infty}\frac{(-1)^{% k}{\left(1-a\right)_{2k}}}{z^{2k}},}}


Constraint(s)

Symbols List

  • ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}} :
  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • f ⁢ ( a , z ) 𝑓 𝑎 𝑧 {\displaystyle{\displaystyle f(a,z)}} : auxiliary function (locally)
  •  Edit this on Wikidata

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