Abstract. The one variable Krawtchouk polynomials, a special case of the 2F1 function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the F1 Appel function shows up in th...

Basilar membrane responses to pairs of tones were measured, with the use of a laser velocimeter, in the basal turn of the cochlea in anesthetized chinchillas. Frequency spectra of basilar membrane responses to primary tones with frequencies (f1, f2) close to the characteristic frequency (CF) contain prominent odd-order two-tone distortion products (DPs) at frequencies both higher and lower than...

tions F(3), F(4), Lauricella’s quadruple hypergeometric function F A , Exton’s multiple hypergeometric functions X E:G;H , K10, K13, X8, (k)H 2 , (k)H 4 , Erdélyi’s multiple hypergeometric function Hn,k, Khan and Pathan’s triple hypergeometric function H (P) 4 , Kampé de Fériet’s double hypergeometric function F E:G;H , Appell’s double hypergeometric function of the second kind F2, and the Sriv...

Each family of Gauss hypergeometric functions fn = 2F1(a + ε1n, b + ε2n; c + ε3n; z), for fixed εj = 0,±1 (not all εj equal to zero) satisfies a second order linear difference equation of the form Anfn−1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different εj values) can be transformed into each other. We give a...

We investigate the zeros of a family of hypergeometric polynomials 2F1(−n,−x; a; t), n ∈ N that are known as the Meixner polynomials for certain values of the parameters a and t. When a = −N, N ∈ N and t = p , the polynomials Kn(x; p,N) = (−N)n2F1(−n,−x;−N; p ), n = 0, 1, . . .N, 0 < p < 1 are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polyno...

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1, . . . , 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions 0F1, 1F1, a Humbert function Ψ1, and a Humbert function Φ2. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric f...

In this paper, we obtain the extended Wright generalized Hypergeometric function using extended Beta function. We also obtain certain integral representations, Mellin transform and some derivative properties of extended Wright generalized Hypergeometric function. Further, we represent extended Wright generalized Hypergeometric function in the form of Laguerre polynomials and Whittaker function.