Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.6922)

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=2, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=2, b₁=6

http://functions.wolfram.com/07.25.03.6922.01

Input Form

HypergeometricPFQ[{-(7/2), 2}, {6, 6}, z] == (320 (-384 + 2448 z - 3060 z^2 + 1105 z^3))/(21879 z^5) + (1/(50262517305 z^5)) (1024 E^(z/2) (275675400 - 1895268375 z + 2957954040 z^2 - 1555547400 z^3 + 191280240 z^4 + 70769520 z^5 - 23870400 z^6 + 2697024 z^7 - 131200 z^8 + 2304 z^9) BesselI[0, z/2]) - (1/(50262517305 z^4)) (1024 E^(z/2) (-539117415 + 1772397000 z - 1311753960 z^2 + 233364240 z^3 + 50569200 z^4 - 21363264 z^5 + 2569280 z^6 - 128896 z^7 + 2304 z^8) BesselI[1, z/2])

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]