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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), -(11/2)}, z] == (1/306338830875) (E^z (306338830875 - 167093907750 z + 92142319500 z^2 + 12180861000 z^3 + 91159992000 z^4 + 629108726400 z^5 + 38029014777600 z^6 + 2123792264563200 z^7 + 12121282461657600 z^8 + 22756235412556800 z^9 + 19757842988083200 z^10 + 9315019858636800 z^11 + 2606913843609600 z^12 + 456052513996800 z^13 + 51259611217920 z^14 + 3730966708224 z^15 + 173616070656 z^16 + 4952031232 z^17 + 78381056 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]