Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anp5)

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.anp5.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(3/2), 2}, z] == (1/2679075) (E^(z/2) (2679075 - 28312200 z + 392934780 z^2 + 3385572120 z^3 + 6611245200 z^4 + 5409270720 z^5 + 2220099840 z^6 + 494774784 z^7 + 61668096 z^8 + 4239360 z^9 + 148480 z^10 + 2048 z^11) BesselI[0, z/2]) + (1/2679075) (E^(z/2) (-165375 + 4747680 z - 43057980 z^2 + 874886040 z^3 + 3435269040 z^4 + 3775947840 z^5 + 1806223104 z^6 + 439036416 z^7 + 57645312 z^8 + 4093952 z^9 + 146432 z^10 + 2048 z^11) 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]