Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anp7)

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=-3/2

http://functions.wolfram.com/07.25.03.anp7.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(3/2), 3}, z] == (1/2679075) (4 E^(z/2) (675675 - 4819500 z + 49589820 z^2 + 334252800 z^3 + 514417680 z^4 + 328224960 z^5 + 102816000 z^6 + 16889856 z^7 + 1463040 z^8 + 62464 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(2679075 z)) (4 E^(z/2) (-23625 - 70875 z + 1035720 z^2 - 6545700 z^3 + 103980240 z^4 + 299703600 z^5 + 246818880 z^6 + 87941376 z^7 + 15517440 z^8 + 1402112 z^9 + 61440 z^10 + 1024 z^11) 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]