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

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=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(7/2), 2}, z] == (1/10418625) (E^(z/2) (10418625 - 41674500 z + 103326300 z^2 - 274012200 z^3 + 1616842080 z^4 + 7459925760 z^5 + 8170848000 z^6 + 3857656320 z^7 + 925666560 z^8 + 120013824 z^9 + 8414208 z^10 + 296960 z^11 + 4096 z^12) BesselI[0, z/2]) + (1/10418625) (E^(z/2) (-1488375 + 14156100 z - 39482100 z^2 + 92330280 z^3 - 286907040 z^4 + 3049079040 z^5 + 5400380160 z^6 + 3088995840 z^7 + 817415424 z^8 + 112032768 z^9 + 8123392 z^10 + 292864 z^11 + 4096 z^12) 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]