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

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, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-1/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(1/2), 2}, z] == (1/184320) (184320 - 5529600 z - 46198215 z^2 - 77331450 z^3 - 49689396 z^4 - 15157464 z^5 - 2393680 z^6 - 198624 z^7 - 8128 z^8 - 128 z^9) + (1/368640) (E^z Sqrt[Pi] (-31216185 z^(3/2) - 142702560 z^(5/2) - 193667760 z^(7/2) - 112569600 z^(9/2) - 32529120 z^(11/2) - 4978176 z^(13/2) - 405248 z^(15/2) - 16384 z^(17/2) - 256 z^(19/2)) 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]