Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj5r)

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=-9/2

http://functions.wolfram.com/07.25.03.aj5r.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(9/2), 7/2}, -z] == (-30240 - 10080 z - 2457 z^2 - 360 z^3 + 60 z^4 + 108 z^5 + 126 z^6 + 358 z^7 - 120 z^8 + 8 z^9)/(567 z^2) + (1/(567 z^(5/2))) ((Sqrt[Pi] (15120 + 15120 z + 7560 z^2 + 2520 z^3 + 630 z^4 + 126 z^5 + 21 z^6 + 3 z^7 - 414 z^8 + 124 z^9 - 8 z^10) Erfi[Sqrt[z]])/E^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]