Generalized hypergeometric function 4F3: Specific values (formula 07.28.03.0068)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

For fixed a₁, a₂, a₃, z

http://functions.wolfram.com/07.28.03.0068.01

Input Form

HypergeometricPFQ[{a, b, c, a + b - c}, {(a + b)/2, (a + b + 1)/2, a + b}, z] == (1 - 2 (Sqrt[-1 + z] Sqrt[z] + z))^a Hypergeometric2F1[a, c, a + b, 2 (Sqrt[-1 + z] Sqrt[z] + z)] Hypergeometric2F1[a, a + b - c, a + b, 2 (Sqrt[-1 + z] Sqrt[z] + 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},{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]