Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9t)

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=-9/2

http://functions.wolfram.com/07.25.03.al9t.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(9/2), 6}, z] == -((1/(99225 z^3)) (32 E^(z/2) (5237832600 - 2515538025 z + 766215450 z^2 - 174567960 z^3 + 31963680 z^4 - 4903920 z^5 + 648480 z^6 - 75840 z^7 + 9216 z^8 + 1792 z^9 + 512 z^10) BesselI[0, z/2])) - (1/(99225 z^4)) (32 E^(z/2) (-20951330400 + 10062152100 z - 3719590875 z^2 + 1012701690 z^3 - 216798120 z^4 + 38152800 z^5 - 5693520 z^6 + 736800 z^7 - 83904 z^8 + 8192 z^9 + 1280 z^10 + 512 z^11) 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]