Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.all5)

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=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.all5.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(9/2), 6}, z] == -((1/(893025 z^3)) (32 E^(z/2) (-5237832600 + 2722294575 z - 871620750 z^2 + 207805500 z^3 - 39765600 z^4 + 6365520 z^5 - 870240 z^6 + 96000 z^7 + 15360 z^8 + 55040 z^9 + 14848 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(893025 z^4)) (32 E^(z/2) (20951330400 - 10889178300 z + 4141212075 z^2 - 1171620450 z^3 + 261330300 z^4 - 47990880 z^5 + 7487760 z^6 - 1019040 z^7 + 126720 z^8 - 20480 z^9 + 41728 z^10 + 13824 z^11 + 1024 z^12) 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]