\\% q-exponential and q-trigonometric series.
\\ Author: Joerg Arndt
\\ License: GPL version 3 or later
\\ online at http://www.jjj.de/pari/
\\ version: 2011-August-11 (12:42)

read("eta.gpi");  \\ for Etax() and Etax_plus()

read("qtrig1.gpi");  \\ First kind
read("qtrig1r.gpi");  \\ First kind, regularized
read("qtrig2.gpi");  \\ Scond kind
read("qtrig2r.gpi");  \\ Scond kind, regularized


\\ Connection between exponentials of the first and second kind:
\\ exp_q(q, x) = exp_Q(q, x/(1-q))
\\ Exp_q(q, x) = Exp_Q(q, x/(1-q))
\\ rexp_q(q, x/2) - rexp_Q(q, x/(1-q))
\\
\\ exp_Q(q, x) = exp_q(q, x*(1-q))
\\ Exp_Q(q, x) = Exp_q(q, x*(1-q))
\\ rexp_Q(q, x/2) = rexp_q(q, x*(1-q))

\\ For the files qtrig1.gpi, qtrig2.gpi, qtrig2.gpi, qtrig2r.gpi:
\\
\\ With some formulas we use Ek to denote prod(n>=1, 1-q^(k*n) ).
\\ For example, exp_q(+q^2,-q) = E1*E4 / E2^2.
\\ An remark [Somos's t8_18_60a] denotes the formula identifier
\\ in Michael Somos' database of "Dedekind Eta Function Product Identities",
\\ online at http://eta.math.georgetown.edu/
\\
\\ Remarks of the form [cf. A103446] give sequence numbers
\\ for the On-Line Encyclopedia of Integer Sequences (OEIS),
\\ online at http://oeis.org/

\\ q-derivative:
Qderiv(f, q, x, qs, xs, S=-1)={ (f(q,q*x,S)-f(q,x,S))/(qs*xs-xs); }


\\ ==== end of file ====