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International Journal of Scientific and Research Publications, Volume 2, Issue 10, October 2012 39
ISSN 2250-3153
1
H 4 (β 1 , α 2 , α 1 + 2 , γ 3 ;
2
cosh
4(2 − cosh
x
x
This leads to Erdelyi’s (1948) when y = 0
To prove these we know that
F K (α 1 , α 2 , α 2 , β 1 , β 2 ,β 1 ; γ 1 , γ 2, γ 3; cosh x, cosh y, cosh z)
(
)
(
)(
∞
α
1 m
α
2
β1
m+
p
β2
n
∑
m, n=
o m ! n!
p!(
γ
1)
m
( γ
2)
n(
γ
3)
p
)
absolutely convergent if p = (1-m) (1-n) where
|cosh x|< 1, |cosh y|