THE OBJECT OF THIS PAPER IS TO FIND CONDITIONS OF L (T) SO THAT (FORMULA) AS APPLICATIONS, FOR SPECIFIC VALUES OF L (T), VL (F) (Z) FOUND THAT SEVERAL KNOWN INTEGRAL OPRETIONS CARRY PG (B) INTO M (0,M).

IN THIS PAPER A GENERALIZED MATRIX GAMMA DISTRIBUTION INCLUDING GENERALIZED Hypergeometric function AND ZONAL POLYNOMIALS IS INTRODUCED. SOME IMPORTANT STATISTICAL CHARACTERISTICS SUCH AS THE LAPLACE TRANSFORMATION AND EXPECTATION OF DETERMINANT ARE GIVEN.

WE STUDY PROPERTIES OF STARLIKE AND CONVEXITY FOR THE Hypergeometric function F (A, B; C; Z) DEFINED BY RUSCHEWEYH DERIVATIVE THROUGH PUTTING CONDITIONS ON A, B, C, TO ENSURE THAT ZF (A, B; C; Z) WILL BE IN VARIOUS SUBCLASSES OF STARLIKE AND CONVEX functionS.

IN THIS PAPER, WE FINDING CONDITIONS ON THE TRIPLET (A, B, C) SO THAT THE function ZF(A, B; C; Z) IS STARLIKE IN D, WHERE F (A, B; C; Z) DENOTES THE HYPER GEOMETRIC function.ALSO THE GEOMETRIC PROBLEM OF STAR LIKENESS AND CLOSE TO CONVEXITY OF ZF (A, B; C; Z) IS STUDIED.