Generalized hypergeometric function 3F2: Identities (formula 07.27.17.0018)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Identities

Functional identities

Relations between contiguous functions

http://functions.wolfram.com/07.27.17.0018.01

Input Form

(a + z (Subscript[a, 2] + Subscript[a, 3] - d - e)) HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3]}, {d, e}, z] + (((d - a) (d - Subscript[a, 2]) (d - Subscript[a, 3]) z)/(d (d - e))) HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3]}, {d + 1, e}, z] + (((e - a) (e - Subscript[a, 2]) (e - Subscript[a, 3]) z)/(e (e - d))) HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3]}, {d, e + 1}, z] == a (1 - z) HypergeometricPFQ[{a + 1, Subscript[a, 2], Subscript[a, 3]}, {d, e}, z]

Standard Form

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MathML Form

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Rule 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,a₄},{b₁,b₂,b₃},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]