Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1556)

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=-1/2

http://functions.wolfram.com/07.25.03.1556.01

Input Form

HypergeometricPFQ[{-(11/2), 5/2}, {-(1/2), 5}, z] == -((1/(43648605 z^2)) (32 E^(z/2) (-654885 - 363825 z - 1330560 z^2 - 6694380 z^3 + 23693232 z^4 - 17206608 z^5 + 4407360 z^6 - 438784 z^7 + 14336 z^8) BesselI[0, z/2])) + (1/(43648605 z^3)) (32 E^(z/2) (-2619540 - 1455300 z + 51975 z^2 + 457380 z^3 + 1342668 z^4 + 11894208 z^5 - 13414416 z^6 + 3990080 z^7 - 424448 z^8 + 14336 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]