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

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=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(7/2), -(7/2)}, z] == (1/31255875) (31255875 + 70166250 z + 218918700 z^2 + 1702701000 z^3 + 115783668000 z^4 + 6225853233600 z^5 + 32905818691200 z^6 + 57722872354560 z^7 + 47340854611200 z^8 + 21295549785600 z^9 + 5735971906560 z^10 + 972845475840 z^11 + 106659434496 z^12 + 7610974080 z^13 + 348685440 z^14 + 9826048 z^15 + 154112 z^16 + 1024 z^17) + (1/31255875) (64 E^z Sqrt[Pi] (13232419200 z^(9/2) + 215327548800 z^(11/2) + 793389945600 z^(13/2) + 1172534227200 z^(15/2) + 874599314400 z^(17/2) + 371590662240 z^(19/2) + 96518187360 z^(21/2) + 15980677920 z^(23/2) + 1723471425 z^(25/2) + 121571745 z^(27/2) + 5523792 z^(29/2) + 154728 z^(31/2) + 2416 z^(33/2) + 16 z^(35/2)) 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]