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

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=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(5/2), 1/2}, z] == (1/14175) (14175 - 187110 z + 1081080 z^2 - 10810800 z^3 - 36186480 z^4 - 31009440 z^5 - 11187456 z^6 - 1976832 z^7 - 177920 z^8 - 7744 z^9 - 128 z^10) - (1/14175) (32 E^z Sqrt[Pi] (665280 z^(7/2) + 1496880 z^(9/2) + 1118880 z^(11/2) + 378000 z^(13/2) + 64440 z^(15/2) + 5679 z^(17/2) + 244 z^(19/2) + 4 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]