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

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, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(5/2), 1}, z] == (1/1382400) (1382400 - 16588800 z + 116121600 z^2 - 1445068800 z^3 - 6670007775 z^4 - 8061128280 z^5 - 4283007240 z^6 - 1189595520 z^7 - 186445440 z^8 - 16918400 z^9 - 872832 z^10 - 23552 z^11 - 256 z^12) + (1/2764800) (E^z Sqrt[Pi] (-6335611425 z^(7/2) - 18928616850 z^(9/2) - 19558234800 z^(11/2) - 9604360800 z^(13/2) - 2550693600 z^(15/2) - 388992960 z^(17/2) - 34686720 z^(19/2) - 1768960 z^(21/2) - 47360 z^(23/2) - 512 z^(25/2)) 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]