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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), -(7/2)}, z] == (1/156279375) (156279375 + 420997500 z + 1532430900 z^2 + 13621608000 z^3 + 1042053012000 z^4 + 63105407164800 z^5 + 375744968726400 z^6 + 743451424773120 z^7 + 690473300486400 z^8 + 354112053120000 z^9 + 109821380981760 z^10 + 21742691604480 z^11 + 2835973773312 z^12 + 247299704640 z^13 + 14405615040 z^14 + 550043648 z^15 + 13138944 z^16 + 177152 z^17 + 1024 z^18) + (1/156279375) (32 E^z Sqrt[Pi] (251415964800 z^(9/2) + 4548343363200 z^(11/2) + 18678623846400 z^(13/2) + 30900135571200 z^(15/2) + 25959249943200 z^(17/2) + 12525327833760 z^(19/2) + 3735245132640 z^(21/2) + 720398746080 z^(23/2) + 92282855715 z^(25/2) + 7945097415 z^(27/2) + 458571378 z^(29/2) + 17391432 z^(31/2) + 413344 z^(33/2) + 5552 z^(35/2) + 32 z^(37/2)) 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]