Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8084)

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=5, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=5, b₁=3

http://functions.wolfram.com/07.25.03.8084.01

Input Form

HypergeometricPFQ[{-(7/2), 5}, {3, 6}, z] == (1/(6891885 z^3)) (4 E^(z/2) (10080 - 5040 z + 1575 z^2 + 1751610 z^3 - 2431380 z^4 + 982752 z^5 - 140816 z^6 + 6240 z^7) BesselI[0, z/2]) - (1/(6891885 z^4)) (4 E^(z/2) (40320 - 20160 z + 7560 z^2 + 113925 z^3 + 421050 z^4 - 1641132 z^5 + 851296 z^6 - 134576 z^7 + 6240 z^8) 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]