Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1904)

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=-11/2, a₂>=-11/2

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

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

http://functions.wolfram.com/07.25.03.1904.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {-(3/2), 4}, z] == (1/(34459425 z)) (4 E^(z/2) (-654885 + 9251550 z + 22577940 z^2 + 96477120 z^3 - 298790400 z^4 + 178372608 z^5 - 33546240 z^6 + 1835008 z^7) BesselI[0, z/2]) - (1/(34459425 z^2)) (4 E^(z/2) (-2619540 + 2546775 z - 3097710 z^2 - 8644140 z^3 - 20942400 z^4 - 165232128 z^5 + 147578880 z^6 - 31711232 z^7 + 1835008 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]