Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1745)

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=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=2

http://functions.wolfram.com/07.25.03.1745.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {2, 5}, z] == (1/(218243025 z^2)) (8 E^(z/2) (-124740 - 135135 z + 27359640 z^2 - 57629880 z^3 + 38789040 z^4 - 11088816 z^5 + 1471296 z^6 - 88384 z^7 + 1920 z^8) BesselI[0, z/2]) - (1/(218243025 z^3)) (8 E^(z/2) (-498960 - 540540 z + 301455 z^2 + 4074840 z^3 - 31704360 z^4 + 29657136 z^5 - 9744336 z^6 + 1385792 z^7 - 86464 z^8 + 1920 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]