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DLMF:17.2.E15

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Formula:6002
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MaRDI QIDQ6002

  • Label: DLMF:17.2.E15


Digital Library of Mathematical Functions ID 17.2.E15

( a ⁒ q - n ; q ) k = ( a ; q ) k ⁒ ( q / a ; q ) n ( q 1 - k / a ; q ) n ⁒ q - n ⁒ k , q-Pochhammer-symbol π‘Ž superscript π‘ž 𝑛 π‘ž π‘˜ q-Pochhammer-symbol π‘Ž π‘ž π‘˜ q-Pochhammer-symbol π‘ž π‘Ž π‘ž 𝑛 q-Pochhammer-symbol superscript π‘ž 1 π‘˜ π‘Ž π‘ž 𝑛 superscript π‘ž 𝑛 π‘˜ {\displaystyle{\displaystyle\left(aq^{-n};q\right)_{k}=\frac{\left(a;q\right)_% {k}\left(q/a;q\right)_{n}}{\left(q^{1-k}/a;q\right)_{n}}q^{-nk},}}


Constraint(s)

Symbols List

  • ( a ; q ) n q-Pochhammer-symbol π‘Ž π‘ž 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}} :
  • k π‘˜ {\displaystyle{\displaystyle k}} : nonnegative integer
  • q π‘ž {\displaystyle{\displaystyle q}} : complex base
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
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