Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2700)

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=-1/2

http://functions.wolfram.com/07.25.03.2700.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {-(1/2), 5}, z] == -((1/(218243025 z^2)) (32 E^(z/2) (-31185 + 48510 z - 6891390 z^2 - 78906960 z^3 + 445807680 z^4 - 501230592 z^5 + 194568192 z^6 - 28377088 z^7 + 1310720 z^8) BesselI[0, z/2])) + (1/(218243025 z^3)) (64 E^(z/2) (-62370 + 97020 z - 144540 z^2 + 415305 z^3 + 5339640 z^4 + 80810016 z^5 - 172647936 z^6 + 84078592 z^7 - 13533184 z^8 + 655360 z^9) 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]