Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amx2)

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=9/2, a₂>=9/2

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

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

http://functions.wolfram.com/07.25.03.amx2.01

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(9/2), -(7/2)}, z] == -((1/9845600625) (E^z (-9845600625 - 5626057500 z - 21057529500 z^2 - 111449520000 z^3 - 2787095304000 z^4 + 190859874912000 z^5 + 3978179757216000 z^6 + 15097941879552000 z^7 + 22250462072025600 z^8 + 16397687348582400 z^9 + 6861803968051200 z^10 + 1753748759347200 z^11 + 285699747594240 z^12 + 30326069329920 z^13 + 2106476789760 z^14 + 94301061120 z^15 + 2604072960 z^16 + 40108032 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]