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

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=2, a₂>=2

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

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

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

Input Form

HypergeometricPFQ[{2, 5/2}, {-(11/2), 11/2}, z] == (1/(33 z^4)) (101606400 - 19353600 z + 5806080 z^2 - 1128960 z^3 + 173217 z^4 - 21300 z^5 + 2100 z^6 - 160 z^7 + 8 z^8) + (1/(33 z^(9/2))) (4 E^z Sqrt[Pi] (-12700800 + 10886400 z - 4596480 z^2 + 1270080 z^3 - 257040 z^4 + 40320 z^5 - 5040 z^6 + 504 z^7 - 39 z^8 + 2 z^9) 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]