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

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=1/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {1/2, 1/2}, z] == (1440 + 65610 z + 207060 z^2 + 180369 z^3 + 62172 z^4 + 9592 z^5 + 656 z^6 + 16 z^7)/1440 + (1/2880) (E^z Sqrt[Pi] (20790 Sqrt[z] + 249480 z^(3/2) + 550935 z^(5/2) + 414810 z^(7/2) + 133320 z^(9/2) + 19824 z^(11/2) + 1328 z^(13/2) + 32 z^(15/2)) 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]