Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an4e)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-1/2

http://functions.wolfram.com/07.25.03.an4e.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(1/2), 1/2}, z] == (1/6300) (6300 - 680400 z - 12058200 z^2 - 33873840 z^3 - 33513480 z^4 - 15246660 z^5 - 3599635 z^6 - 463800 z^7 - 32512 z^8 - 1152 z^9 - 16 z^10) + (1/12600) (E^z Sqrt[Pi] (-5405400 z^(3/2) - 43243200 z^(5/2) - 91891800 z^(7/2) - 79579500 z^(9/2) - 33700485 z^(11/2) - 7633290 z^(13/2) - 959000 z^(15/2) - 66160 z^(17/2) - 2320 z^(19/2) - 32 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]