restart:
read "qFPS.mpl":
with(qFPS):
<Text-field style="Heading 1" layout="Heading 1">discrete q-Hermite II</Text-field>
P:=DiscreteqHermiteII(n,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=-I);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">Al-Salam-Carlitz II</Text-field>
P:=AlSalamCarlitzII(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">q-Charlier</Text-field>
P:=qCharlier(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qpochhammer(-q/a,q,n)*qphihypergeom([q^(-n)],[-q/a],-q^(n+1)*x/a,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qpochhammer(-q/a,q,n)*qphihypergeom([q^(-n)],[-q/a],-q^(n+1)*x/a,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">q-Laguerre</Text-field>
P:=qLaguerre(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qpochhammer(q^(a+1),q,n)/qpochhammer(q,q,n)*qphihypergeom([q^(-n)],[q^(a+1)],-q^(n+a+1)*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qpochhammer(q^(a+1),q,n)/qpochhammer(q,q,n)*qphihypergeom([q^(-n)],[q^(a+1)],-q^(n+a+1)*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=-1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">Stieltjes-Wigert</Text-field>
P:=StieltjesWigert(n,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(1/qpochhammer(q,q,n)*qphihypergeom([q^(-n)],[0],-q^(n+1)*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(1/qpochhammer(q,q,n)*qphihypergeom([q^(-n)],[0],-q^(n+1)*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">q-Meixner</Text-field>
P:=qMeixner(n,b,c,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">Quantum-q-Krawtchouk</Text-field>
P:=QuantumqKrawtchouk(n,p,N,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">q-Krawtchouk</Text-field>
P:=qKrawtchouk(n,p,N,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">affine q-Krawtchouk</Text-field>
P:=AffineqKrawtchouk(n,p,N,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,expansionpt=q^(-N));
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">little q-Laguerre</Text-field>
P:=LittleqLaguerre(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qphihypergeom([q^(-n),0],[a*q],q*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qphihypergeom([q^(-n),0],[a*q],q*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">alternative q-Charlier</Text-field>
P:=AlternativeqCharlier(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qphihypergeom([q^(-n),-a*q^n],[0],q*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qphihypergeom([q^(-n),-a*q^n],[0],q*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">little q-Jacobi</Text-field>
P:=LittleqJacobi(n,a,b,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qphihypergeom([q^(-n),a*b*q^(n+1)],[a*q],q*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qphihypergeom([q^(-n),a*b*q^(n+1)],[a*q],q*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">little q-Legendre</Text-field>
P:=LittleqLegendre(n,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qphihypergeom([q^(-n),q^(n+1)],[q],q*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qphihypergeom([q^(-n),q^(n+1)],[q],q*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">discrete q-Hermite I</Text-field>
P:=DiscreteqHermiteI(n,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">Al-Salam-Carlitz I</Text-field>
P:=AlSalamCarlitzI(n,a,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">big q-Laguerre</Text-field>
P:=BigqLaguerre(n,a,b,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
PS:=convert(P,qFPS,x,expansionpt=a*q,initialcheck=false);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">q-Hahn</Text-field>
P:=qHahn(n,a,b,N,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">big q-Jacobi</Text-field>
P:=BigqJacobi(n,a,b,c,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);
<Text-field style="Heading 1" layout="Heading 1">big q-Legendre</Text-field>
P:=BigqLegendre(n,c,x,q):
q-shift rules
qshift(P,x,q);
qshift(P,x,1/q);
q-derivative rules
qdiff(P,x,q);
qdiff(P,x,1/q);
q-holonomic recurrence equation
qHolonomicRE(P,F(x));
qHolonomicRE(qphihypergeom([q^(-n),q^(n+1)],[q],q*x,q),F(x));
q-holonomic difference equation
qHolonomicDE(P,F(x));
qHolonomicDE(qphihypergeom([q^(-n),q^(n+1)],[q],q*x,q),F(x));
q-hypergeometric series
PS:=convert(P,qFPS,x,base=qpochhammer,expansionpt=1);
convert(PS,qphihypergeom);