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

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.ajsc.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), 1/2}, z] == (1/42525) (42525 - 283500 z + 661500 z^2 - 1270080 z^3 + 2993760 z^4 - 17297280 z^5 - 30933630 z^6 - 16724430 z^7 - 4138599 z^8 - 529872 z^9 - 35952 z^10 - 1216 z^11 - 16 z^12) + (1/85050) (E^z Sqrt[Pi] (-55552770 z^(11/2) - 75494790 z^(13/2) - 37136925 z^(15/2) - 8774010 z^(17/2) - 1094520 z^(19/2) - 73104 z^(21/2) - 2448 z^(23/2) - 32 z^(25/2)) 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]