Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj5h)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.aj5h.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(9/2), 1/2}, z] == (1/8505) (8505 - 37800 z + 63000 z^2 - 90720 z^3 + 166320 z^4 - 768768 z^5 - 917280 z^6 - 318240 z^7 - 45968 z^8 - 2880 z^9 - 64 z^10) - (1/8505) (8 E^z Sqrt[Pi] (139230 z^(11/2) + 132090 z^(13/2) + 42483 z^(15/2) + 5922 z^(17/2) + 364 z^(19/2) + 8 z^(21/2)) 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]