Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anpy)

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=1/2

http://functions.wolfram.com/07.25.03.anpy.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {1/2, 4}, z] == (1/(297675 z)) (4 E^(z/2) (135 + 74520 z + 1089000 z^2 + 2562480 z^3 + 2131920 z^4 + 769344 z^5 + 128448 z^6 + 9600 z^7 + 256 z^8) BesselI[0, z/2]) + (1/(297675 z^2)) (4 E^(z/2) (-540 - 405 z - 2520 z^2 + 199080 z^3 + 1267920 z^4 + 1528464 z^5 + 654528 z^6 + 119232 z^7 + 9344 z^8 + 256 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]