Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajc9)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ajc9.01

Input Form

HypergeometricPFQ[{5/2, 9/2}, {-(9/2), 3}, z] == -((1/297675) (8 E^(z/2) (-87885 + 65205 z - 37800 z^2 + 25200 z^3 - 25200 z^4 + 67536 z^5 + 151872 z^6 + 56832 z^7 + 6912 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(297675 z)) (4 E^(z/2) (405405 - 124740 z + 1890 z^2 + 25200 z^3 - 25200 z^4 + 24192 z^5 - 35616 z^6 + 209280 z^7 + 100608 z^8 + 13312 z^9 + 512 z^10) 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]