Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak0x)

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=-11/2

http://functions.wolfram.com/07.25.03.ak0x.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(11/2), -(1/2)}, z] == (1/155925) (155925 + 595350 z - 2381400 z^2 + 4158000 z^3 - 6486480 z^4 + 12972960 z^5 - 65345280 z^6 - 92828160 z^7 - 39755520 z^8 - 7565824 z^9 - 703488 z^10 - 30976 z^11 - 512 z^12) - (1/155925) (128 E^z Sqrt[Pi] (771120 z^(13/2) + 856800 z^(15/2) + 337680 z^(17/2) + 61740 z^(19/2) + 5615 z^(21/2) + 244 z^(23/2) + 4 z^(25/2)) 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]