Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3905)

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=3/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.3905.01

Input Form

HypergeometricPFQ[{-(9/2), 3/2}, {-(5/2), 11/2}, -z] == (1/(122880 z^4)) ((3472875 - 1512000 z + 415800 z^2 - 30240 z^3 + 11040 z^4 - 5376 z^5 + 4224 z^6 - 9728 z^7 - 1280 z^8)/E^z) + (1/(245760 z^(9/2))) (Sqrt[Pi] (-3472875 + 3827250 z - 2041200 z^2 + 635040 z^3 - 20736 z^8 - 2560 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]