Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah0c)

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=-9/2

http://functions.wolfram.com/07.25.03.ah0c.01

Input Form

HypergeometricPFQ[{3/2, 5}, {-(9/2), 9/2}, z] == (1/(432 z^3)) (-302400 + 146160 z - 50760 z^2 + 13968 z^3 - 3180 z^4 + 630 z^5 - 123 z^6 + 38 z^7 - 60 z^8 - 8 z^9) + (1/(864 z^(7/2))) (E^z Sqrt[Pi] (302400 - 347760 z + 201960 z^2 - 78480 z^3 + 22860 z^4 - 5310 z^5 + 1023 z^6 - 168 z^7 + 24 z^8 - 128 z^9 - 16 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]