Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj6m)

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=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-7/2

http://functions.wolfram.com/07.25.03.aj6m.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(7/2), 11/2}, z] == (2116800 - 630000 z + 185400 z^2 - 42480 z^3 + 7896 z^4 - 1230 z^5 + 165 z^6 - 20 z^7 + 4 z^8)/(4 z^4) + (1/(8 z^(9/2))) (E^z Sqrt[Pi] (-2116800 + 2041200 z - 981720 z^2 + 313920 z^3 - 75060 z^4 + 14310 z^5 - 2265 z^6 + 306 z^7 - 36 z^8 + 8 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]