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

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), -(5/2)}, z] == (1/12658629375) (E^z (12658629375 + 21379018500 z + 109252678500 z^2 + 1932363216000 z^3 - 51468245640000 z^4 + 1241233308000000 z^5 + 16288205607072000 z^6 + 46090373075712000 z^7 + 54919632156480000 z^8 + 34309019840256000 z^9 + 12551511545395200 z^10 + 2865786425671680 z^11 + 423765666938880 z^12 + 41330557255680 z^13 + 2663365017600 z^14 + 111476736000 z^15 + 2896625664 z^16 + 42205184 z^17 + 262144 z^18))

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]