Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak2w)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ak2w.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(7/2), 11/2}, z] == (3 (1411200 - 394800 z + 115920 z^2 - 26040 z^3 + 4735 z^4 - 720 z^5 + 94 z^6 - 11 z^7 + 2 z^8))/(5 z^4) + (1/(10 z^(9/2))) (3 E^z Sqrt[Pi] (-1411200 + 1335600 z - 630000 z^2 + 197400 z^3 - 46200 z^4 + 8610 z^5 - 1330 z^6 + 175 z^7 - 20 z^8 + 4 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]