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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{-(3/2), 6}, {-(9/2), -(1/2)}, z] == (1/37800) (37800 - 151200 z + 119070 z^2 - 36330 z^3 - 21357 z^4 + 131805 z^5 + 64820 z^6 + 10632 z^7 + 704 z^8 + 16 z^9) + (1/75600) (E^z Sqrt[Pi] (-270270 z^(3/2) + 270270 z^(5/2) - 135135 z^(7/2) + 45045 z^(9/2) + 319410 z^(11/2) + 139608 z^(13/2) + 21952 z^(15/2) + 1424 z^(17/2) + 32 z^(19/2)) 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]