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Journal of Inequalities and Applications

Table 1 The coefficients A ℓ and B ℓ

From: Reduction formulae for the Lauricella functions in several variables

ℓ

A ℓ

B ℓ

5

− ( b + a + 6 ) 2 + 1 4 ( b − a + 6 ) 2 + 1 2 (b−a+6)(b+a+6)+11(b+a+6)− 13 2 (b−a+6)−20

( b + a + 6 ) 2 − 1 4 ( b − a + 6 ) 2 + 1 2 (b−a+6)(b+a+6)−17(b+a+6)− 1 2 (b−a+6)+62

4

1 2 (b+a+1)(b+a−3)− 1 4 (b−a+3)(b−a−3)

−2(b + a − 1)

3

− 1 2 (3a+b−2)

1 2 (3b+a−2)

2

1 2 (b+a−1)

−2

1

−1

1

0

1

0

−1

1

1

−2

1 2 (b+a−1)

2

−3

1 2 (3a+b−2)

1 2 (3b+a−2)

−4

1 2 (b+a+1)(b+a−3)− 1 4 (b−a+3)(b−a−3)

2(b + a − 1)

−5

( b + a − 4 ) 2 − 1 4 ( b − a − 4 ) 2 − 1 2 (b+a−4)(b−a−4)+4(b+a−4)− 7 2 (b−a−4)

( b + a − 4 ) 2 − 1 4 ( b − a − 4 ) 2 + 1 2 (b+a−4)(b−a−4)+8(b+a−4)− 1 2 (b−a−4)+12

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