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Formula:5861

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Digital Library of Mathematical Functions ID 15.12.E4

( e t - 1 t ) b - 1 ⁢ e t ⁢ ( 1 - c ) ⁢ ( 1 - z + z ⁢ e - t ) - a = ∑ s = 0 ∞ q s ⁢ ( z ) ⁢ t s . superscript superscript 𝑒 𝑡 1 𝑡 𝑏 1 superscript 𝑒 𝑡 1 𝑐 superscript 1 𝑧 𝑧 superscript 𝑒 𝑡 𝑎 superscript subscript 𝑠 0 subscript 𝑞 𝑠 𝑧 superscript 𝑡 𝑠 {\displaystyle{\displaystyle\left(\frac{e^{t}-1}{t}\right)^{b-1}e^{t(1-c)}% \left(1-z+ze^{-t}\right)^{-a}=\sum_{s=0}^{\infty}q_{s}(z)t^{s}.}}


Constraint(s)

Symbols List

  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • s 𝑠 {\displaystyle{\displaystyle s}} : nonnegative integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : real or complex parameter
  • b 𝑏 {\displaystyle{\displaystyle b}} : real or complex parameter
  • c 𝑐 {\displaystyle{\displaystyle c}} : real or complex parameter
  • q s ⁢ ( z ) subscript 𝑞 𝑠 𝑧 {\displaystyle{\displaystyle q_{s}(z)}} : coefficients
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