Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7805)

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=9/2, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=9/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.7805.01

Input Form

HypergeometricPFQ[{-(7/2), 9/2}, {-(3/2), 6}, z] == (1/(2297295 z^3)) (32 E^(z/2) (1081080 - 363825 z + 60480 z^2 + 77280 z^3 + 76800 z^4 + 178176 z^5 - 327680 z^6 + 65536 z^7) BesselI[0, z/2]) - (1/(2297295 z^4)) (32 E^(z/2) (4324320 - 1455300 z + 377055 z^2 - 23520 z^3 - 45600 z^4 - 39936 z^5 - 51200 z^6 - 262144 z^7 + 65536 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]