Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amy2)

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=-5/2

http://functions.wolfram.com/07.25.03.amy2.01

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(5/2), 1}, z] == (1/1488375) (E^(z/2) (1488375 - 15479100 z + 94537800 z^2 - 990654840 z^3 - 7130176200 z^4 - 12064227840 z^5 - 8741537280 z^6 - 3228664320 z^7 - 655909632 z^8 - 75310080 z^9 - 4810752 z^10 - 157696 z^11 - 2048 z^12) BesselI[0, z/2]) - (1/1488375) (4 E^(z/2) (-718200 z + 5266485 z^2 - 31865400 z^3 + 525415590 z^4 + 1669631040 z^5 + 1576169280 z^6 + 668118528 z^7 + 146839680 z^8 + 17682432 z^9 + 1164032 z^10 + 38912 z^11 + 512 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]