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

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=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 4}, z] == -((1/(4465125 z)) (4 E^(z/2) (-93555 - 1122660 z + 3874500 z^2 - 10924200 z^3 + 63488880 z^4 + 279353088 z^5 + 282030336 z^6 + 117434880 z^7 + 23549184 z^8 + 2368512 z^9 + 113664 z^10 + 2048 z^11) BesselI[0, z/2])) - (1/(4465125 z^2)) (4 E^(z/2) (374220 + 25515 z + 253260 z^2 - 1379700 z^3 + 3651480 z^4 - 11459952 z^5 + 118653696 z^6 + 193653504 z^7 + 97113600 z^8 + 21345024 z^9 + 2257920 z^10 + 111616 z^11 + 2048 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]