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

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=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), -(5/2)}, z] == (1/7016625) (7016625 + 7654500 z + 13891500 z^2 + 95256000 z^3 - 943034400 z^4 + 5448643200 z^5 - 59935075200 z^6 - 247439923200 z^7 - 281676672000 z^8 - 146569489920 z^9 - 41384367360 z^10 - 6869750400 z^11 - 694869360 z^12 - 42988800 z^13 - 1576192 z^14 - 31232 z^15 - 256 z^16) - (1/7016625) (8 E^z Sqrt[Pi] (15725707200 z^(13/2) + 43245694800 z^(15/2) + 42551913600 z^(17/2) + 20565946800 z^(19/2) + 5564863800 z^(21/2) + 899690265 z^(23/2) + 89451690 z^(25/2) + 5470200 z^(27/2) + 198960 z^(29/2) + 3920 z^(31/2) + 32 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]