Generalized hypergeometric function 4F3: Identities (formula 07.28.17.0018)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]

Identities

Functional identities

Relations between contiguous functions

http://functions.wolfram.com/07.28.17.0018.01

Input Form

(a + z Sum[Subscript[a, j + 1] - Subscript[b, j], {j, 1, 3}]) HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + z Sum[(((Subscript[b, j] - a) Product[Subscript[b, j] - Subscript[a, k + 1], {k, 1, 3}])/(Subscript[b, j] Product[If[k == j, 1, Subscript[b, j] - Subscript[b, k]], {k, 1, 3}])) HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, j - 1], Subscript[b, j] + 1, Subscript[b, j + 1], \[Ellipsis], Subscript[b, 3]}, z], {j, 1, 3}] == a (1 - z) HypergeometricPFQ[{a + 1, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z]

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]