ISSN (e): 2250 – 3005 || Vol, 04 || Issue, 10 || October – 2014 || International Journal of Computational Engineering Research (IJCER) www.ijceronline.com Open Access Journal Page 24 On The Derivatives and Partial Derivatives of A Certain Generalized Hyper geometric Function 1 Yashwant Singh, 2 Nandavasanthnadiger Kulkarni 1 Department of Mathematics, Government College, Kaladera, Jaipur, Rajasthan, India 2 Department of Mathematics, Dayananda Sagar college of arts, science and commerce, Kumaraswamy layout, Bangalore, Karnataka, India I. INTRODUCTION The H -function of two variables defined and represented by Singh and Mandia [12] in the following manner: 1 2 2 3 2 1, 1, 1, 1, 1, 1 2 2 2 3 3 3 1 1 2 2 2 2 1, 1, 1, 1, 1, 1 2 2 2 3 3 3 , ; , , ; , , , , ; , , , : , : , , : , ; , , ; , , , , ; , , , , ; , j j j j j j j j j j j j j p n n p n n p j j j j j j j j j j j j j q m m q m m q a A c K c e E R e E on m n m n x x p q p q p q y y b B d d L f F f F S H x y H H = 1 2 1 2 3 2 1 , ( ) ( ) 4 L L x yd d (1.1) Where 1 1 1 1 1 1 1 1 1 , 1 n j j j j p q j j j j j j j n j a A a A b B (1.2) 2 2 2 2 2 2 1 1 2 1 1 1 1 j j n m K j j j j j j p q L j j j j j n j m c d c d (1.3) 3 3 3 3 3 3 1 1 3 1 1 1 1 j j n m R j j j j j j p q S j j j j j n j m e E f F e E f F (1.4) ABSTRACT In this paper, methods involving derivatives and the Mellin transformation are employed in obtaining finite summations for the H -function of two variables and certain special partial derivatives for the H -function of two variables with respect to parameters. KEY WORDS: Derivatives, Partial derivatives, H -function of two variables, Mellin transformation. (2000 Mathematics Subject Classification: 33C99)