Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ao0a)

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=1/2

http://functions.wolfram.com/07.25.03.ao0a.01

Input Form

HypergeometricPFQ[{6, 6}, {1/2, 1}, -z] == (1/7372800) (7372800 - 422785575 z + 2342173050 z^2 - 3866064720 z^3 + 2728624320 z^4 - 971991840 z^5 + 189657920 z^6 - 20916480 z^7 + 1286144 z^8 - 40704 z^9 + 512 z^10) + (1/14745600) ((Sqrt[Pi] (-108056025 Sqrt[z] + 1920996000 z^(3/2) - 7155710100 z^(5/2) + 9816681600 z^(7/2) - 6281642400 z^(9/2) + 2115586560 z^(11/2) - 399043200 z^(13/2) + 43079680 z^(15/2) - 2612480 z^(17/2) + 81920 z^(19/2) - 1024 z^(21/2)) 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]