Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae0p)

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.ae0p.01

Input Form

HypergeometricPFQ[{1/2, 5}, {-(7/2), -(5/2)}, z] == (1/4725) (4725 + 1350 z + 1620 z^2 + 12600 z^3 - 352800 z^4 - 2059920 z^5 - 2339160 z^6 - 1007544 z^7 - 201150 z^8 - 19780 z^9 - 920 z^10 - 16 z^11) + (1/4725) (E^z Sqrt[Pi] (-875160 z^(9/2) - 2903940 z^(11/2) - 2763180 z^(13/2) - 1099305 z^(15/2) - 210600 z^(17/2) - 20232 z^(19/2) - 928 z^(21/2) - 16 z^(23/2)) 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]