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

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=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-3/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(3/2), -(1/2)}, z] == (1/945) (945 + 28350 z - 1871100 z^2 - 24864840 z^3 - 58378320 z^4 - 50738688 z^5 - 20865000 z^6 - 4535220 z^7 - 544902 z^8 - 35956 z^9 - 1208 z^10 - 16 z^11) + (1/945) E^z Sqrt[Pi] (-6486480 z^(5/2) - 42162120 z^(7/2) - 77117040 z^(9/2) - 59443020 z^(11/2) - 22899870 z^(13/2) - 4791129 z^(15/2) - 562296 z^(17/2) - 36552 z^(19/2) - 1216 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]