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

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=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(7/2), 5}, z] == (1/(31255875 z^2)) (32 E^(z/2) (6081075 - 2432430 z + 1769040 z^2 - 2268000 z^3 + 3061800 z^4 - 5171040 z^5 + 20901888 z^6 + 68207616 z^7 + 47934720 z^8 + 13392384 z^9 + 1708032 z^10 + 98304 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/(31255875 z^3)) (64 E^(z/2) (-12162150 + 4864860 z - 1964655 z^2 + 334530 z^3 + 396900 z^4 - 714420 z^5 + 1061424 z^6 - 2270592 z^7 + 17978112 z^8 + 18412800 z^9 + 5912832 z^10 + 806400 z^11 + 48128 z^12 + 1024 z^13) 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]