Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4906)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=2

http://functions.wolfram.com/07.25.03.4906.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {2, 5}, z] == -((1/(11486475 z^2)) (16 E^(z/2) (-1890 + 945 z - 718200 z^2 + 1629495 z^3 - 1099680 z^4 + 286464 z^5 - 29952 z^6 + 1040 z^7) BesselI[0, z/2])) + (1/(11486475 z^3)) (8 E^(z/2) (-15120 + 7560 z - 2835 z^2 - 173250 z^3 + 1755690 z^4 - 1710048 z^5 + 516144 z^6 - 57824 z^7 + 2080 z^8) 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]