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QHypergeometricPFQ

QHypergeometricPFQ[{a1, ..., ar}, {b1, ..., bs}, q, z]
gives the basic hypergeometric series _rphi_s(a;b;q;z).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • _rphi_s(a;b;q;z) has series expansion sum_(k=0)^infty(a_1;q)_k...(a_r;q)_k/(b_1;q)_k...(b_s;q)_k ((-1)^kq^(k(k-1)/2))^(1+s-r)z^k/(q;q)_k.
  • The basic hypergeometric series is defined for |q|<1.
  • For r=s+1, the basic hypergeometric series is defined for |z|<1.
EXAMPLESCLOSE ALL
Scope   (4)
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
TraditionalForm formatting:
Applications   (3)
Two natural q-extensions of exponential function:
q-binomial theorem:
q-analog of Legendre polynomial:
Properties & Relations   (2)
QHypergeometricPFQ is not closed under differentiation with respect to z:
It is closed under q-difference:
Series expansions:
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