Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2500)

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=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=1

http://functions.wolfram.com/07.25.03.2500.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {1, 6}, z] == (1/(916620705 z^3)) (E^(z/2) (7983360 - 3991680 z + 1247400 z^2 + 916329645 z^3 - 4659434010 z^4 + 5801519304 z^5 - 2713986912 z^6 + 541441680 z^7 - 45932640 z^8 + 1343680 z^9) BesselI[0, z/2]) + (1/(916620705 z^4)) (E^(z/2) (-31933440 + 15966720 z - 5987520 z^2 + 1663200 z^3 - 363825 z^4 + 1630010214 z^5 - 3772478472 z^6 + 2237413152 z^7 - 497524560 z^8 + 44588960 z^9 - 1343680 z^10) 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]