Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7660)

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=4, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=4, b₁=2

http://functions.wolfram.com/07.25.03.7660.01

Input Form

HypergeometricPFQ[{-(7/2), 4}, {2, 5}, z] == (1/(2027025 z^2)) (8 E^(z/2) (1260 - 630 z + 253575 z^2 - 472080 z^3 + 245100 z^4 - 43296 z^5 + 2288 z^6) BesselI[0, z/2]) - (1/(2027025 z^3)) (8 E^(z/2) (5040 - 2520 z + 945 z^2 + 37275 z^3 - 285060 z^4 + 205236 z^5 - 41008 z^6 + 2288 z^7) 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]