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

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=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), 9/2}, z] == (1/255150) (255150 - 415800 z + 491400 z^2 - 604800 z^3 + 1028160 z^4 - 4596480 z^5 - 5400990 z^6 - 1983945 z^7 - 330060 z^8 - 27192 z^9 - 1072 z^10 - 16 z^11) - (1/510300) (E^z Sqrt[Pi] z^(11/2) (13226850 + 12514635 z + 4273290 z^2 + 686280 z^3 + 55440 z^4 + 2160 z^5 + 32 z^6) 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]