Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1361)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=2, b₁=3/2

http://functions.wolfram.com/07.25.03.1361.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {3/2, 5}, -z] == -((4 (90 - 228 z + 323 z^2))/(20995 z^4)) + (1/(15116400 z^4)) ((259200 - 397440 z + 403200 z^2 + 645120 z^3 + 9247365 z^4 + 8317890 z^5 + 2553048 z^6 + 339120 z^7 + 19856 z^8 + 416 z^9)/E^z) + (1/(30232800 Sqrt[z])) (Sqrt[Pi] (6235515 + 24942060 z + 18895500 z^2 + 5426400 z^3 + 697680 z^4 + 40128 z^5 + 832 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]