Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2104)

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=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=1

http://functions.wolfram.com/07.25.03.2104.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {1, 9/2}, -z] == (1/(226492416 z^3)) ((-779625 - 1081080 z - 2079000 z^2 + 190358208 z^3 + 576577536 z^4 + 387641472 z^5 + 93535104 z^6 + 8919040 z^7 + 282880 z^8)/ E^z) + (1/(452984832 z^(7/2))) (Sqrt[Pi] (779625 + 561330 z + 1496880 z^2 + 34927200 z^3 + 733471200 z^4 + 1466942400 z^5 + 860606208 z^6 + 195706368 z^7 + 18120960 z^8 + 565760 z^9) 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]