Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1530)

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=5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.1530.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(3/2), 3}, z] == (1/1216215) (4 E^(z/2) (322245 + 748440 z + 3139452 z^2 - 9620736 z^3 + 5675520 z^4 - 1056768 z^5 + 57344 z^6) BesselI[0, z/2]) - (1/(1216215 z)) (4 E^(z/2) (72765 - 114345 z - 290412 z^2 - 686724 z^3 - 5358336 z^4 + 4704768 z^5 - 999424 z^6 + 57344 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]