Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1058)

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=1, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.1058.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {11/2, 6}, -z] == -((3 (120 + 2520 z + 7980 z^2 + 9044 z^3 + 4845 z^4))/(4199 z^5)) + (1/(21670871040 z^5)) ((1857945600 + 27125492625 z + 62670935250 z^2 + 53632378800 z^3 + 22205383200 z^4 + 5026301280 z^5 + 659305920 z^6 + 50983680 z^7 + 2271744 z^8 + 53504 z^9 + 512 z^10)/E^z) + (1/(43341742080 z^(9/2))) (Sqrt[Pi] (13749310575 + 91662070500 z + 164991726900 z^2 + 125707982400 z^3 + 48886437600 z^4 + 10666131840 z^5 + 1367452800 z^6 + 104186880 z^7 + 4596480 z^8 + 107520 z^9 + 1024 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]