Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.als2)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-1/2

http://functions.wolfram.com/07.25.03.als2.01

Input Form

HypergeometricPFQ[{7/2, 6}, {-(1/2), -(1/2)}, z] == (1/900) (900 + 75600 z + 3681720 z^2 + 15190560 z^3 + 18872568 z^4 + 10055760 z^5 + 2675075 z^6 + 379032 z^7 + 28736 z^8 + 1088 z^9 + 16 z^10) + (1/1800) (E^z Sqrt[Pi] (1081080 z^(3/2) + 15135120 z^(5/2) + 43397640 z^(7/2) + 45851520 z^(9/2) + 22470045 z^(11/2) + 5703018 z^(13/2) + 785752 z^(15/2) + 58544 z^(17/2) + 2192 z^(19/2) + 32 z^(21/2)) 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]