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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Contiguous relation coefficients

From: Relations between Lauricella’s triple hypergeometric function F A ( 3 ) (x,y,z) and Exton’s function X 8

j

A j

B j

5

−4 ( 1 − α − 2 n ) 2 +2(1−α)(1−α−2n)+ ( 1 − α ) 2 +22(1−α−2n)−13(1−α)−20

4 ( α + 2 n ) 2 −2(1−α)(α+2n)+ ( 1 − α ) 2 +34(α+2n)+(1−α)+62

4

2(α + 1 + 2n)(α + 3 + 2n)−α(α + 3)

4(α + 2n + 3)

3

−α − 4n − 2

−3α − 4n − 6

2

−α − 1 − 2n

−2

1

−1

1

0

1

0

−1

1

1

−2

1 − α − 2n

2

−3

1 − α − 4n

3 − 3α − 4n

−4

2(1 − 2α − n)(3 − α − 2n)−(1 − α)(4 − α)

4(1 − α − 2n)

−5

4 ( 1 − α − 2 n ) 2 −2(1−α)(1−α−2n) − ( 1 − α ) 2 +8(1−α−2n)+7α−7

4 ( α + 2 n ) 2 +2(1−α)(α+2n)− ( 1 − α ) 2 −16(α+2n)+α−1

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