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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), 2}, z] == (1/1031443875) (E^(z/2) (1031443875 - 2783261250 z + 3991226400 z^2 - 4724697600 z^3 + 5883645600 z^4 - 9909345600 z^5 + 42092265600 z^6 + 149509463040 z^7 + 122829315840 z^8 + 44222492160 z^9 + 8271943680 z^10 + 854138880 z^11 + 48623616 z^12 + 1417216 z^13 + 16384 z^14) BesselI[0, z/2]) + (1/1031443875) (E^(z/2) (-212837625 + 1225825650 z - 2057529600 z^2 + 2489356800 z^3 - 2907122400 z^4 + 4037947200 z^5 - 8838668160 z^6 + 73769149440 z^7 + 88798913280 z^8 + 37096604160 z^9 + 7486617600 z^10 + 807591936 z^11 + 47230976 z^12 + 1400832 z^13 + 16384 z^14) 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]