Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2565)

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=6

http://functions.wolfram.com/07.25.03.2565.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {6, 6}, z] == 10240/(29393 z^5) + (1/(80826697146195 z^5)) (64 E^(z/2) (-439977938400 + 219988969200 z + 97807965885 z^2 + 77131363995 z^3 + 66126299400 z^4 + 1330169725080 z^5 - 1484553223440 z^6 + 563702113296 z^7 - 98100545088 z^8 + 8450445120 z^9 - 347093760 z^10 + 5374720 z^11) BesselI[0, z/2]) - (1/(80826697146195 z^4)) (64 E^(z/2) (501226348140 + 326857870080 z + 276158305395 z^2 + 278479882800 z^3 + 454681672200 z^4 - 1045238838336 z^5 + 477278280528 z^6 - 90154616448 z^7 + 8111413440 z^8 - 341719040 z^9 + 5374720 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]