SALAHUDDIN / IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org Vol. 1, Issue 1, pp. 022-027
CONSTRUCTION OF A SUMMATION FORMULA INTERLACED WITH CONTIGUOUS RELATION SALAHUDDIN P.D.M College of Engineering , Bahadurgarh , Haryana , India
Abstract The main aim of this paper is to develop a summation formula interlaced with Hypergeometric function and contiguous relation. 2010 MSC NO : 33C05 , 33C20 , 33D15 , 33D50 , 33D60
Key words: Contiguous relation, Recurrence relation, Legendre’s duplication formula. A Introduction Generalized Gaussian Hypergeometric function of one variable
where the parameters b1 , b2 , ….,bB are neither zero nor negative integers and A , B are non negative integers. Contiguous Relation : [Abramowitz p.558(15.2.19)] (a-b) (1-z) 2F1(a, b ; c; z) = (c-b) 2F1(a,b-1; c; z) + (a-c) 2F1(a-1,b; c; z)
(2)
Legendre’s duplication formula :
Recurrence relation Γ(ζ+1) = ζ Γ(ζ)
(6)
B MAIN SUMMATION FORMULAE For the formula a ≠ b
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