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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(9/2), 6}, z] == -((1/(6251175 z^3)) (32 E^(z/2) (15713497800 - 7960127175 z + 2505402900 z^2 - 588602700 z^3 + 111245400 z^4 - 17735760 z^5 + 2540160 z^6 - 449280 z^7 + 483840 z^8 + 1040640 z^9 + 408576 z^10 + 52224 z^11 + 2048 z^12) BesselI[0, z/2])) - (1/(6251175 z^4)) (32 E^(z/2) (-62853991200 + 31840508700 z - 11985798825 z^2 + 3348645300 z^3 - 736589700 z^4 + 133199640 z^5 - 20366640 z^6 + 2643840 z^7 - 241920 z^8 - 84480 z^9 + 704256 z^10 + 359424 z^11 + 50176 z^12 + 2048 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]