Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1397)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=7/2

http://functions.wolfram.com/07.25.03.1397.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {7/2, 5}, z] == (12 (-6 - 76 z + 323 z^2))/(4199 z^4) + (1/(902952960 z^4)) (E^z (15482880 + 180633600 z - 367141005 z^2 - 205890930 z^3 + 395966340 z^4 - 162927864 z^5 + 29162640 z^6 - 2552416 z^7 + 106176 z^8 - 1664 z^9)) + (1/(1805905920 z^(5/2))) (Sqrt[Pi] (-654729075 + 698377680 z + 698377680 z^2 - 931170240 z^3 + 352716000 z^4 - 60775680 z^5 + 5209344 z^6 - 214016 z^7 + 3328 z^8) Erfi[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]