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

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), -(5/2)}, z] == (1/49116375) (49116375 + 64297800 z + 130977000 z^2 + 972972000 z^3 - 10216206000 z^4 + 61751289600 z^5 - 703964701440 z^6 - 3033401011200 z^7 - 3583117036800 z^8 - 1928817838080 z^9 - 562198579200 z^10 - 96177758208 z^11 - 10012047360 z^12 - 636733440 z^13 - 23974912 z^14 - 487424 z^15 - 4096 z^16) - (1/49116375) (512 E^z Sqrt[Pi] (2930256000 z^(13/2) + 8351229600 z^(15/2) + 8499466080 z^(17/2) + 4241931120 z^(19/2) + 1183548240 z^(21/2) + 197057070 z^(23/2) + 20154330 z^(25/2) + 1266567 z^(27/2) + 47298 z^(29/2) + 956 z^(31/2) + 8 z^(33/2)) 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]