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

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=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 1}, z] == (1/843908625) (E^(z/2) (843908625 - 6094895625 z + 19632261600 z^2 - 49985586000 z^3 + 146671106400 z^4 - 985620636000 z^5 - 5265434160000 z^6 - 6979533402240 z^7 - 4190817657600 z^8 - 1357280789760 z^9 - 256568739840 z^10 - 29322086400 z^11 - 2033872896 z^12 - 83005440 z^13 - 1818624 z^14 - 16384 z^15) BesselI[0, z/2]) + (1/843908625) (E^(z/2) (1508319225 z - 6882246000 z^2 + 18386449200 z^3 - 46457712000 z^4 + 161431250400 z^5 - 1923865655040 z^6 - 4239670377600 z^7 - 3144404551680 z^8 - 1139200070400 z^9 - 230062325760 z^10 - 27407394816 z^11 - 1953546240 z^12 - 81211392 z^13 - 1802240 z^14 - 16384 z^15) 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]