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

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=7/2, a₂>=7/2

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

For fixed z and a₁=7/2, a₂=11/2, b₁=-3/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(3/2), 4}, z] == (1/(14175 z)) (4 E^(z/2) (2835 + 2520 z - 12600 z^2 + 71280 z^3 + 274320 z^4 + 220224 z^5 + 63168 z^6 + 7040 z^7 + 256 z^8) BesselI[0, z/2]) + (1/(14175 z^2)) (4 E^(z/2) (-11340 + 4095 z - 2520 z^2 + 4680 z^3 - 13680 z^4 + 129744 z^5 + 166848 z^6 + 56512 z^7 + 6784 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]