Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5707)

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=2

http://functions.wolfram.com/07.25.03.5707.01

Input Form

HypergeometricPFQ[{-(9/2), 6}, {2, 9/2}, -z] == (1/(100663296 z^3)) ((8505 + 51030 z + 773388 z^2 + 74498280 z^3 + 140582832 z^4 + 67450656 z^5 + 10933312 z^6 + 537472 z^7)/E^z) + (1/(201326592 z^(7/2))) (Sqrt[Pi] (-8505 - 45360 z - 740880 z^2 + 26671680 z^3 + 244490400 z^4 + 339026688 z^5 + 145297152 z^6 + 22404096 z^7 + 1074944 z^8) 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]