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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(7/2), 4}, z] == (1/(3472875 z)) (4 E^(z/2) (405405 + 782460 z - 1871100 z^2 + 2784600 z^3 - 4813200 z^4 + 19660032 z^5 + 64667904 z^6 + 45918720 z^7 + 12969216 z^8 + 1672192 z^9 + 97280 z^10 + 2048 z^11) BesselI[0, z/2]) + (1/(3472875 z^2)) (4 E^(z/2) (-1621620 + 343035 z - 442260 z^2 + 938700 z^3 - 1348200 z^4 + 1974672 z^5 - 4252416 z^6 + 33897216 z^7 + 35182080 z^8 + 11436800 z^9 + 1577984 z^10 + 95232 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]
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]