Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah6p)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ah6p.01

Input Form

HypergeometricPFQ[{3/2, 11/2}, {-(9/2), 3}, z] == -((1/893025) (8 E^(z/2) (141750 - 70875 z + 25200 z^3 - 36000 z^4 + 98640 z^5 + 211200 z^6 + 70656 z^7 + 7680 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(893025 z)) (4 E^(z/2) (-2027025 + 1559250 z - 708750 z^2 + 252000 z^3 - 90000 z^4 + 47520 z^5 - 55200 z^6 + 302592 z^7 + 126720 z^8 + 14848 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]