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

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=5/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{5/2, 5/2}, {-(9/2), 1}, z] == (1/8505) (E^(z/2) (8505 - 16065 z + 14904 z^2 - 13032 z^3 + 15120 z^4 - 44208 z^5 - 106176 z^6 - 44736 z^7 - 6144 z^8 - 256 z^9) BesselI[0, z/2]) + (1/8505) (E^(z/2) (7479 z - 8352 z^2 + 7272 z^3 - 7200 z^4 + 11280 z^5 - 69888 z^6 - 38976 z^7 - 5888 z^8 - 256 z^9) 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]