Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1593)

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=5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5/2, b₁=3/2

http://functions.wolfram.com/07.25.03.1593.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {3/2, 11/2}, -z] == (1/(94371840 z^4)) ((3274425 - 4054050 z + 2328480 z^2 + 2328480 z^3 + 60521760 z^4 + 61055040 z^5 + 19983360 z^6 + 2769408 z^7 + 167168 z^8 + 3584 z^9)/E^z) + (1/(188743680 z^(9/2))) (Sqrt[Pi] (-3274425 + 6237000 z - 5613300 z^2 + 34927200 z^4 + 167650560 z^5 + 139708800 z^6 + 42577920 z^7 + 5702400 z^8 + 337920 z^9 + 7168 z^10) 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]