Generalized hypergeometric function 4F3: Specific values (formula 07.28.03.0038)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Values at z=1

For fixed a₃, a₄

http://functions.wolfram.com/07.28.03.0038.01

Input Form

HypergeometricPFQ[{-(n/2), (1 - n)/2, c, d}, {1/2 - m, c + 1, d + 1}, 1] == (n!/((c - d) Pochhammer[1/2, m])) ((c Pochhammer[d + 1/2, m])/Pochhammer[2 d + 1, n] - (d Pochhammer[c + 1/2, m])/Pochhammer[2 c + 1, n]) /; Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && Floor[n/2] <= m <= 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},{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]