Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.6545)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=1, b₁=11/2

http://functions.wolfram.com/07.25.03.6545.01

Input Form

HypergeometricPFQ[{-(7/2), 1}, {11/2, 6}, -z] == -((5 (168 + 2856 z + 7140 z^2 + 6188 z^3 + 2431 z^4))/(2431 z^5)) + (1/(14936064 z^5)) ((5160960 + 58437855 z + 102901050 z^2 + 65155860 z^3 + 19091160 z^4 + 2862288 z^5 + 224224 z^6 + 8640 z^7 + 128 z^8)/E^z) + (1/(29872128 z^(9/2))) (Sqrt[Pi] (34459425 + 183783600 z + 257297040 z^2 + 147026880 z^3 + 40840800 z^4 + 5940480 z^5 + 456960 z^6 + 17408 z^7 + 256 z^8) 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]