Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8310)

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=-7/2, a₂>=-7/2

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

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

http://functions.wolfram.com/07.25.03.8310.01

Input Form

HypergeometricPFQ[{-(7/2), 6}, {-(11/2), -(5/2)}, z] == (1/89100) (89100 - 136080 z + 176400 z^2 - 403200 z^3 + 293490 z^4 - 57510 z^5 - 289179 z^6 - 104520 z^7 - 14080 z^8 - 800 z^9 - 16 z^10) + (1/178200) (E^z Sqrt[Pi] (-656370 z^(7/2) + 656370 z^(9/2) - 328185 z^(11/2) - 670650 z^(13/2) - 222360 z^(15/2) - 28944 z^(17/2) - 1616 z^(19/2) - 32 z^(21/2)) 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]