Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1181)

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=3/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.1181.01

Input Form

HypergeometricPFQ[{-(11/2), 3/2}, {-(3/2), 6}, z] == (1/(916620705 z^3)) (32 E^(z/2) (-107026920 - 97764975 z - 49958370 z^2 + 11933460 z^3 + 11642400 z^4 + 29876112 z^5 - 64266720 z^6 + 21960192 z^7 - 2426880 z^8 + 81920 z^9) BesselI[0, z/2]) - (1/(916620705 z^4)) (32 E^(z/2) (-428107680 - 391059900 z - 213211845 z^2 - 79064370 z^3 - 7276500 z^4 - 5900832 z^5 - 8085840 z^6 - 45701088 z^7 + 19656192 z^8 - 2344960 z^9 + 81920 z^10) 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]