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

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.ajft.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(11/2), -(11/2)}, z] == (1/972504225) (972504225 + 401861250 z + 208372500 z^2 + 178605000 z^3 + 314344800 z^4 + 1634592960 z^5 + 81729648000 z^6 + 3316494585600 z^7 + 13513012289280 z^8 + 18554822254080 z^9 + 11996838153216 z^10 + 4256755292160 z^11 + 899348889600 z^12 + 118169985024 z^13 + 9824894976 z^14 + 513347328 z^15 + 16224768 z^16 + 281600 z^17 + 2048 z^18) + (1/972504225) (128 E^z Sqrt[Pi] (4102358400 z^(13/2) + 52510187520 z^(15/2) + 153572993280 z^(17/2) + 180984706560 z^(19/2) + 107713277280 z^(21/2) + 36387308160 z^(23/2) + 7453859616 z^(25/2) + 959724864 z^(27/2) + 78701553 z^(29/2) + 4072824 z^(31/2) + 127848 z^(33/2) + 2208 z^(35/2) + 16 z^(37/2)) 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]