Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2172)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=11/2

http://functions.wolfram.com/07.25.03.2172.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {11/2, 6}, -z] == (360 (4 + 21 z))/(4199 z^5) + (1/(69346787328 z^5)) ((-23781703680 - 52390473975 z + 19080723690 z^2 - 12615508080 z^3 + 13118988960 z^4 + 31634751456 z^5 + 13289115840 z^6 + 2313676032 z^7 + 193430016 z^8 + 7631104 z^9 + 113152 z^10)/E^z) + (1/(138693574656 z^(9/2))) (Sqrt[Pi] (-96245174025 - 91662070500 z + 32998345380 z^2 - 25141596480 z^3 + 48886437600 z^4 + 74662922880 z^5 + 28716508800 z^6 + 4813433856 z^7 + 394377984 z^8 + 15375360 z^9 + 226304 z^10) 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]