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

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=-1/2, a₂>=-1/2

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

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

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

Input Form

HypergeometricPFQ[{-(1/2), 11/2}, {-(11/2), 2}, z] == (1/9823275) (E^(z/2) (9823275 - 3638250 z - 1323000 z^2 + 1512000 z^3 - 663600 z^4 + 209760 z^5 - 102720 z^6 - 95488 z^7 - 13568 z^8 - 512 z^9) BesselI[0, z/2]) + (1/9823275) (E^(z/2) (4729725 + 1653750 z - 3969000 z^2 + 2352000 z^3 - 834000 z^4 + 205920 z^5 - 26048 z^6 - 82688 z^7 - 13056 z^8 - 512 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]