Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al98)

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.al98.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(11/2), 5}, z] == (1/(5457375 z^2)) (32 E^(z/2) (-1964187225 + 999323325 z - 314968500 z^2 + 73993500 z^3 - 13935600 z^4 + 2182320 z^5 - 282240 z^6 + 19200 z^7 + 34560 z^8 + 72960 z^9 + 17408 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/(5457375 z^3)) (32 E^(z/2) (7856748900 - 3997293300 z + 1506079575 z^2 - 421621200 z^3 + 92994300 z^4 - 16894080 z^5 + 2615760 z^6 - 359040 z^7 + 49920 z^8 - 15360 z^9 + 57088 z^10 + 16384 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]