Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac6g)

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=5, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.ac6g.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(7/2), 5/2}, z] == (900 + 540 z - 945 z^2 + 507 z^3 - 134 z^4 - 100 z^5 - 8 z^6)/(3360 z) + (E^z Sqrt[Pi] (-900 + 3420 z - 135 z^2 - 1425 z^3 + 960 z^4 - 360 z^5 - 208 z^6 - 16 z^7) Erf[Sqrt[z]])/(6720 z^(3/2))

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]