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

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=5/2, a₂>=5/2

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

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

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(11/2), -(9/2)}, z] == (1/88409475) (88409475 + 44651250 z + 29767500 z^2 + 35721000 z^3 + 104781600 z^4 + 1634592960 z^5 - 81729648000 z^6 - 930464236800 z^7 - 2082982245120 z^8 - 1862153556480 z^9 - 842807153664 z^10 - 216510013440 z^11 - 33508500480 z^12 - 3207945216 z^13 - 189744000 z^14 - 6699264 z^15 - 128512 z^16 - 1024 z^17) - (1/88409475) (64 E^z Sqrt[Pi] (4102358400 z^(13/2) + 24203914560 z^(15/2) + 43123026240 z^(17/2) + 34465420080 z^(19/2) + 14649571440 z^(21/2) + 3622956120 z^(23/2) + 547271928 z^(25/2) + 51556617 z^(27/2) + 3016104 z^(29/2) + 105672 z^(31/2) + 2016 z^(33/2) + 16 z^(35/2)) 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]