Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2564)

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=5, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.2564.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {11/2, 6}, -z] == -(360/(4199 z^5)) + (1/(554774298624 z^5)) ((47563407360 - 48681766665 z + 51280324830 z^2 - 55625134320 z^3 + 78803353440 z^4 + 275726471328 z^5 + 144284578368 z^6 + 29902389504 z^7 + 2894102016 z^8 + 129615616 z^9 + 2149888 z^10)/E^z) + (1/(1109548597248 z^(9/2))) (Sqrt[Pi] (96245174025 - 91662070500 z + 98995036140 z^2 - 125707982400 z^3 + 342205063200 z^4 + 671966305920 z^5 + 315881596800 z^6 + 62574640128 z^7 + 5915669760 z^8 + 261381120 z^9 + 4299776 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]