Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a7ps)

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=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=9/2

http://functions.wolfram.com/07.25.03.a7ps.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {9/2, 5}, -z] == -((40 (3 + 13 z))/(143 z^4)) + (184320 + 307365 z - 100110 z^2 + 69720 z^3 + 79024 z^4 + 14224 z^5 + 672 z^6)/(E^z (219648 z^4)) + (1/(439296 z^(7/2))) (Sqrt[Pi] (675675 + 540540 z - 180180 z^2 + 205920 z^3 + 171600 z^4 + 29120 z^5 + 1344 z^6) 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]