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

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=2, b₁=11/2

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

Input Form

HypergeometricPFQ[{-(1/2), 2}, {11/2, 6}, -z] == (12 (40 + 330 z + 330 z^2 + 77 z^3))/(11 z^5) + (-15360 - 69315 z - 39360 z^2 - 4144 z^3 + 416 z^4 + 48 z^5)/ (E^z (352 z^5)) + (Sqrt[Pi] (-72765 - 173250 z - 83160 z^2 - 7920 z^3 + 880 z^4 + 96 z^5) Erf[Sqrt[z]])/(704 z^(9/2))

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]