Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alk8)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.alk8.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(11/2), -(9/2)}, z] == -((1/139244923125) (E^z (-139244923125 + 30943316250 z - 61886632500 z^2 - 88409475000 z^3 - 462086856000 z^4 - 10543124592000 z^5 + 668837717856000 z^6 + 13030145206848000 z^7 + 46546845162048000 z^8 + 64934612726860800 z^9 + 45509924452608000 z^10 + 18181943023104000 z^11 + 4451281164288000 z^12 + 696592886169600 z^13 + 71205083873280 z^14 + 4773309972480 z^15 + 206624194560 z^16 + 5526650880 z^17 + 82575360 z^18 + 524288 z^19)))

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]