Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8if)

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=6, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.a8if.01

Input Form

HypergeometricPFQ[{-(5/2), 6}, {-(11/2), 11/2}, z] == (-75600 + 47880 z - 22680 z^2 + 10263 z^3 - 1964 z^4 - 120 z^5 + 112 z^6 - 16 z^7)/(5632 z^4) + (1/(11264 z^(9/2))) (E^z Sqrt[Pi] (75600 - 98280 z + 68040 z^2 - 35175 z^3 + 19110 z^4 - 4200 z^5 - 112 z^6 + 208 z^7 - 32 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]