Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajs6)

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=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.ajs6.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), -(5/2)}, z] == (1/637875) (637875 + 850500 z + 1984500 z^2 + 19051200 z^3 - 314344800 z^4 + 5448643200 z^5 + 33269745600 z^6 + 49433198400 z^7 + 31652811360 z^8 + 10605036960 z^9 + 2037336840 z^10 + 234148680 z^11 + 16228320 z^12 + 659136 z^13 + 14336 z^14 + 128 z^15) + (1/637875) (4 E^z Sqrt[Pi] (3333166200 z^(11/2) + 12392541000 z^(13/2) + 15426576900 z^(15/2) + 9041778900 z^(17/2) + 2881041975 z^(19/2) + 536764365 z^(21/2) + 60487650 z^(23/2) + 4137720 z^(25/2) + 166560 z^(27/2) + 3600 z^(29/2) + 32 z^(31/2)) 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]