Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anp3)

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=-3/2

http://functions.wolfram.com/07.25.03.anp3.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(3/2), 1}, z] == (1/2679075) (E^(z/2) (2679075 - 55367550 z + 1167022080 z^2 + 13717226880 z^3 + 35186455080 z^4 + 37478881440 z^5 + 20133308160 z^6 + 5971359744 z^7 + 1021918464 z^8 + 102050304 z^9 + 5799936 z^10 + 172032 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/2679075) (2 E^(z/2) (3002265 z - 48949110 z^2 + 1399798260 z^3 + 7935652620 z^4 + 11951498160 z^5 + 7714973952 z^6 + 2543208192 z^7 + 464034048 z^8 + 48251136 z^9 + 2815488 z^10 + 84992 z^11 + 1024 z^12) 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]