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

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=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(5/2), -(3/2)}, -z] == (1/10125) (10125 - 56700 z + 1190700 z^2 + 69854400 z^3 - 889574400 z^4 + 2114283600 z^5 - 1932035040 z^6 + 864431640 z^7 - 212232420 z^8 + 30207210 z^9 - 2531880 z^10 + 122064 z^11 - 3104 z^12 + 32 z^13) + (1/10125) ((Sqrt[Pi] (-236293200 z^(7/2) + 1509651000 z^(9/2) - 2816424000 z^(11/2) + 2286508500 z^(13/2) - 958108950 z^(15/2) + 226209015 z^(17/2) - 31415850 z^(19/2) + 2591400 z^(21/2) - 123600 z^(23/2) + 3120 z^(25/2) - 32 z^(27/2)) 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]