Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4539)

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, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.4539.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {7/2, 4}, -z] == -(6/(143 z^3)) + (1/(61501440 z^3)) ((2580480 - 3500595 z + 6695640 z^2 + 32562180 z^3 + 19189440 z^4 + 3968304 z^5 + 328064 z^6 + 9152 z^7)/ E^z) + (1/(123002880 z^(5/2))) (Sqrt[Pi] (6081075 - 9459450 z + 34054020 z^2 + 81081000 z^3 + 42042000 z^4 + 8255520 z^5 + 665280 z^6 + 18304 z^7) 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]