On properties and applications of \((p, q)\)-extended \(\tau\)-hypergeometric functions (Q1704665)

The authors introduce \((p,q)\)-extended \(\tau\)-hypergeometric and confluent hypergeometric functions by means of the \((p,q)\)-extended beta function. Then they present a set of Laplace integral representations for \((p,q)\)-extended \(\tau\)-hypergeometric functions. Extending the Mathieu type series they define the Mathieu-type-\(\alpha\)-series and its alternating variant in the form of series by imposing the \((p,q)\)-extended \(\tau\)-hypergeometric function input kernel in the sum and they also establish a contiguous integral form expression for these series.