On solutions to q-difference equations for q-appell functions in the spirit of Olsson and Exton
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Thomas Ernst
Abstract
The purpose of this article is to find many solutions of the canonical q-difference equations for q-Appell functions Φ2, Φ3, Φ4, starting with the first four ones, previously published. Furthermore, q-Laplace integral expressions for two of these functions in the form q-confluent functions are used to find more solutions. In order to explain the discrepancies between meromorphic continuations of multiple q-hypergeometric functions and q-analogues of analytic continuations of corresponding multiple hypergeometric functions, the notion pseudo-meromorphic continuation is introduced to denote equivalence classes of solutions of other q-analogues of systems of partial differential equations. To this end, we introduce equivalence classes of (systems of) partial q-difference equations. Some q-integrals for corresponding q-Appell functions and the second q-Horn function are also proved. In the process, we find a meromorphic continuation of the second q-Horn function. In some formulas, abbreviated notations are used together with combinatorial reasonings. Many proofs use formulas from our first book, which are quoted in detail.
(Communicated by Giuseppe Di Fazio)
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Articles in the same Issue
- Joins of normal matrices, their spectrum, and applications
- On isbell’s density theorem for bitopological pointfree spaces II
- Every positive integer is a sum of at most n + 2 centered n-gonal numbers
- A generalisation of q-additive functions
- Generalised class groups in dihedral and fake ℤp-extensions
- Singular value bounds with applications to norm and numerical radius inequalities
- Coefficient bounds for convex functions associated with cosine function
- On solutions to q-difference equations for q-appell functions in the spirit of Olsson and Exton
- Numerical implementation of solving a boundary value problem including both delay and parameter
- Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions
- Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
- On pseudo almost periodic solutions of the parabolic-elliptic Keller-Segel systems
- A note on derivations into annihilators of the ideals of banach algebras
- Characterization of nonlinear mixed skew lie and jordan n-Type derivation on ∗-Algebras
- Linear and uniformly continuous surjections between Cp-spaces over metrizable spaces
- A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy
- Monotonicity results of ratio between two normalized remainders of Maclaurin series expansion for square of tangent function
