Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8ik)

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=6, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.a8ik.01

Input Form

HypergeometricPFQ[{-(5/2), 6}, {-(9/2), -(7/2)}, z] == (1/198450) (198450 - 189000 z + 113400 z^2 - 40320 z^3 - 60480 z^4 + 725760 z^5 + 1789830 z^6 + 957705 z^7 + 205644 z^8 + 20536 z^9 + 944 z^10 + 16 z^11) + (1/396900) (E^z Sqrt[Pi] (2645370 z^(11/2) + 4375035 z^(13/2) + 2102730 z^(15/2) + 430920 z^(17/2) + 42000 z^(19/2) + 1904 z^(21/2) + 32 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]