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QPolyGamma

QPolyGamma[z, q]
gives the q-digamma function psi_q(z).
QPolyGamma[n, z, q]
gives the n^(th) derivative of the q-digamma function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • psi_q(z)⩵partial_z Gamma_q(z)/Gamma_q(z)⩵-log(1-q)+log(q)sum_(n=0)^inftyq^(n+z)/(1-q^(n+z)).
  • .
EXAMPLESCLOSE ALL
Scope   (6)
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
QPolyGamma threads element-wise over lists:
TraditionalForm formatting:
Applications   (1)
Express certain sums in closed form:
In general all basic q-rational sums can be computed using QPolyGamma:
Use DifferenceDelta to verify:
Properties & Relations   (2)
Differences of QPolyGamma are q-rational functions:
Derivatives of QGamma involve QPolyGamma:
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