Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2631)

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=-7/2

http://functions.wolfram.com/07.25.03.2631.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {-(7/2), 4}, z] == (1/(402026625 z)) (4 E^(z/2) (-1486485 + 103679730 z + 159667200 z^2 + 128163840 z^3 + 115015680 z^4 + 254803968 z^5 - 455081984 z^6 + 83886080 z^7) BesselI[0, z/2]) - (1/(402026625 z^2)) (4 E^(z/2) (-5945940 + 12692295 z - 29168370 z^2 - 94080000 z^3 - 79257600 z^4 - 61145088 z^5 - 74448896 z^6 - 371195904 z^7 + 83886080 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]