Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al94)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.al94.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(11/2), 3}, z] == (1/16372125) (16 E^(z/2) (1403325 - 1488375 z + 1039500 z^2 - 689850 z^3 + 529200 z^4 - 584640 z^5 + 1693440 z^6 + 4129920 z^7 + 1854720 z^8 + 311040 z^9 + 21504 z^10 + 512 z^11) BesselI[0, z/2]) + (1/(16372125 z)) (4 E^(z/2) (-6081075 + 2759400 z^2 - 2457000 z^3 + 1701000 z^4 - 1229760 z^5 + 1128960 z^6 - 1728000 z^7 + 10725120 z^8 + 6297600 z^9 + 1161216 z^10 + 83968 z^11 + 2048 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]
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HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
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HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
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HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]