Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajth)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.ajth.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(7/2), 11/2}, z] == (1/(320 z^4)) (-2116800 + 932400 z - 303480 z^2 + 78480 z^3 - 16500 z^4 + 2790 z^5 - 285 z^6 - 136 z^7 + 576 z^8 + 224 z^9 + 16 z^10) + (1/(640 z^(9/2))) (E^z Sqrt[Pi] (2116800 - 2343600 z + 1301400 z^2 - 482400 z^3 + 134100 z^4 - 29790 z^5 + 5505 z^6 - 870 z^7 + 120 z^8 + 1360 z^9 + 464 z^10 + 32 z^11) Erf[Sqrt[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)

2007-05-02

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