Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9567)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9567.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 13/4}, -z] == (Sqrt[Pi] z^(1/4) (49841250834375 - 223288803738000 z + 1190873619936000 z^2 + 814272560640000 z^3 + 109482024960000 z^4 + 4549902336000 z^5 + 64709722112 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-17223157880775 + 44501921402400 z + 45402184154880 z^2 + 6590406574080 z^3 + 280639242240 z^4 + 4028628992 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + 4 (4077261619200 - 17816458950675 z + 67086823557600 z^2 + 49715933218560 z^3 + 6790923632640 z^4 + 283617460224 z^5 + 4041211904 z^6 + 16777216 z^7) Sin[2 Sqrt[z]]))/ (1185465080217600 z^(5/2))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]