Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.0117)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

For fixed a₁,a₂,a₃,b₂,z

http://functions.wolfram.com/07.27.03.0117.01

Input Form

HypergeometricPFQ[{a, b, c}, {a - n, e}, z] == (1/Pochhammer[1 - a, n]) Sum[(((-1)^k Pochhammer[1 - a, n - k] Pochhammer[b, k] Pochhammer[c, k])/ Pochhammer[e, k]) Binomial[n, k] Hypergeometric2F1[b + k, c + k, e + k, z] z^k, {k, 0, n}]

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]