Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3575)

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=1/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.3575.01

Input Form

HypergeometricPFQ[{-(9/2), 1/2}, {-(3/2), 11/2}, -z] == (1/(393216 z^4)) ((-496125 + 519750 z - 381780 z^2 + 279720 z^3 + 20208 z^4 - 17376 z^5 + 43584 z^6 + 10112 z^7 + 512 z^8)/E^z) + (1/(786432 z^(9/2))) (Sqrt[Pi] (496125 - 850500 z + 816480 z^2 - 635040 z^3 + 635040 z^4 + 96768 z^7 + 20736 z^8 + 1024 z^9) 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]