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

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=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 5}, {-(11/2), 11/2}, z] == (1/(528 z^4)) (63504000 - 23889600 z + 7439040 z^2 - 1857240 z^3 + 381672 z^4 - 66420 z^5 + 10020 z^6 - 1337 z^7 + 162 z^8 - 20 z^9 + 8 z^10) + (1/(1056 z^(9/2))) (E^z Sqrt[Pi] (-63504000 + 66225600 z - 34655040 z^2 + 12138840 z^3 - 3202920 z^4 + 679140 z^5 - 120540 z^6 + 18417 z^7 - 2472 z^8 + 296 z^9 - 32 z^10 + 16 z^11) 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]