Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1725)

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=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=1

http://functions.wolfram.com/07.25.03.1725.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {1, 6}, z] == (1/(305540235 z^3)) (8 E^(z/2) (1995840 + 1621620 z + 384615 z^2 + 37837800 z^3 - 123991560 z^4 + 108192336 z^5 - 36656592 z^6 + 5474496 z^7 - 358592 z^8 + 8320 z^9) BesselI[0, z/2]) - (1/(305540235 z^4)) (8 E^(z/2) (7983360 + 6486480 z + 1787940 z^2 - 1216215 z^3 + 582120 z^4 - 56959896 z^5 + 78737232 z^6 - 31695024 z^7 + 5128384 z^8 - 350272 z^9 + 8320 z^10) 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]