Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa8v)

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=5, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.aa8v.01

Input Form

HypergeometricPFQ[{-(3/2), 5}, {-(7/2), -(5/2)}, z] == (1/3150) (3150 - 2700 z + 1080 z^2 + 1680 z^3 - 20160 z^4 - 48030 z^5 - 23515 z^6 - 4266 z^7 - 316 z^8 - 8 z^9) + (1/6300) (E^z Sqrt[Pi] (-72930 z^(9/2) - 116025 z^(11/2) - 51000 z^(13/2) - 8840 z^(15/2) - 640 z^(17/2) - 16 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]